Messages from 2008
These are the messages distributed to the Banach list during 2008.
From banach-bounces at math.okstate.edu Fri Jan 4 12:00:27 2008
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From: Dale Alspach <alspach at math.okstate.edu>
Subject: [Banach] Conference on Convex Geometry
Reply-To: koldobsk at math.missouri.edu
Dear Colleagues,
We would like to invite you to participate in the Conference on
Convex Geometry in Columbia, Missouri in March 2008. There will
be two mini-conferences - Classical Convex Geometry on March 21-23
and Asymptotic Convex Geometry on March 28-30.
Please see the conference homepage at
http://www.math.missouri.edu/calendar/FRG-08
which contains the list of speakers, accomodations and directions
to Columbia, Missouri.
Please take a minute to register at the website above.
Best regards,
Alex Koldobsky and Mark Rudelson
_______________________________________________
Banach mailing list
Banach at math.okstate.edu
http://hardy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Wed Jan 16 10:38:31 2008
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id 545EFD0A4B; Wed, 16 Jan 2008 10:38:31 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Emanuel Milman
Message-Id: <20080116163831.545EFD0A4B at fourier.math.okstate.edu>
Date: Wed, 16 Jan 2008 10:38:31 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On the role of convexity in
isoperimetry, spectral-gap and concentration" by Emanuel Milman.
Abstract: We show that for convex domains in Euclidean space, Cheeger's
isoperimetric inequality, Spectral-Gap of the Neumann Laplacian,
Exponential concentration of 1-Lipschitz functions, and the a-priori
weakest linear tail-decay of 1-Lipschitz functions, are all equivalent (to
within universal constants). This substantially extends previous results
of Maz'ya, Cheeger, Gromov--Milman, Buser and Ledoux. As an application,
we conclude the stability of the Spectral-Gap for convex domains under
convex perturbations which preserve volume (up to constants) and under
maps which are ``on-average'' Lipschitz. We also easily recover (and
extend) many previously known lower bounds, due to Payne--Weinberger,
Li--Yau, Kannan--Lov\'asz--Simonovits, Bobkov and Sodin, on the Cheeger
constant for convex domains. We also provide a new characterization
of the Cheeger constant, as one over the expectation of the distance
from the ``worst'' Borel set having half the measure of the convex
domain. As a by-product of our methods, we develop a coherent single
framework for passing between isoperimetric inequalities, Orlicz-Sobolev
functional inequalities and q-capacities, the latter being notions
introduced by Maz'ya and extended by Barthe--Cattiaux--Roberto. As
an application, we extend the known results due to the latter authors
about the stability of the isoperimetric profile under tensorization,
when there is no Central-Limit obstruction. A crucial ingredient to
our proof is a result from Riemannian Geometry on the concavity of the
isoperimetric profile. Our results extend to the more general setting
of Riemannian manifolds with density which satisfy the $CD(0,\infty)$
curvature-dimension condition of Bakry-\'Emery.
Archive classification: math.MG math.FA
Remarks: 70 pages, 1st version
The source file(s), Dingir120.eps: 7755 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0712.4092
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http://arXiv.org/abs/0712.4092
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From alspach at fourier.math.okstate.edu Fri Jan 18 08:24:42 2008
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id 5B414D09C3; Fri, 18 Jan 2008 08:24:42 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Heinz H. Bauschke, Xianfu Wang, Jane Ye, and Xiaoming Yuan
Message-Id: <20080118142442.5B414D09C3 at fourier.math.okstate.edu>
Date: Fri, 18 Jan 2008 08:24:42 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Bregman distances and Chebyshev
sets" by Heinz H. Bauschke, Xianfu Wang, Jane Ye, and Xiaoming Yuan.
Abstract: A closed set of a Euclidean space is said to be Chebyshev
if every point in the space has one and only one closest point in the
set. Although the situation is not settled in infinite-dimensional
Hilbert spaces, in 1932 Bunt showed that in Euclidean spaces a closed
set is Chebyshev if and only if the set is convex. In this paper, from
the more general perspective of Bregman distances, we show that if every
point in the space has a unique nearest point in a closed set, then the
set is convex. We provide two approaches: one is by nonsmooth analysis;
the other by maximal monotone operator theory. Subdifferentiability
properties of Bregman nearest distance functions are also given.
Archive classification: math.FA
Mathematics Subject Classification: Primary 41A65; Secondary 47H05, 49J52.
The source file(s), submitted.tex: 67922 bytes, is(are) stored in gzipped
form as 0712.4030.gz with size 19kb. The corresponding postcript file
has gzipped size 134kb.
Submitted from: heinz.bauschke at ubc.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0712.4030
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http://arXiv.org/abs/0712.4030
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From banach-bounces at math.okstate.edu Thu Jan 17 21:59:11 2008
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From: "George A Anastassiou (ganastss)" <ganastss at memphis.edu>
To: anna <anna at eureka.vu.edu.au>, atnet <at-net-dl at uni-giessen.de>, banach
<banach at math.okstate.edu>, Dynamics <hsg at phy.duke.edu>, dynsys
<dynsys at listserv.unc.edu>, "George A Anastassiou (ganastss)"
<ganastss at memphis.edu>, nanet <na.digest at na-net.ornl.gov>, rgmia
<rgmia at lists.vu.edu.au>, rgmia-request <rgmia-request at lists.vu.edu.au>,
siam <helfrich at siam.org>, stochastic <bulletin at queue.Korea.ac.kr>
Date: Thu, 17 Jan 2008 12:40:52 -0600
Thread-Topic: AMAT08
Thread-Index: AchZOHzIncKDYRr1ScSBez4jXBUo9A==
Message-ID: <06CF1FBD4645F745B5A89221FF341DC324A6AE7D at itexbe7.uom.memphis.edu>
Subject: [Banach] AMAT08
DEAR COLLEAQUES HI!
CONFERENCE ANNOUNCEMENT:
"International Conference on Applied Mathematics and Approximation Theory
2008", October 11-13,2008, University of Memphis, Memphis, TN, USA.
Honoring 80th Birthday of P.L.Butzer (AMAT08).
Plenary Speakers:C.Bardaro, J.Bona, B.Berndt, F.Deutsch, K.Diethelm, S.Dragomir, J.Goldstein, M.Ismail, M.J.Lai, H.Mhaskar, J.Prestin, S.Samko, R.Stens, A.Zayed.
Organizer:George Anastassiou, http://www.msci.memphis.edu/AMAT2008/
PLEASE REGISTER-COME
THANKS
SINCERELY YOURS
George A. Anastassiou,Ph.D
DOCTOR HONORIS CAUSA
Professor of Mathematics
Department of Mathematical Sciences
The University of Memphis,Memphis,TN 38152,USA
Editor-In-Chief JoCAAA, JCAAM,JAFA ;World Sci.Publ.Book Series:
Concrete & Applicable Math.
Springer Consultant-Editor in computational math books
Birkhauser Consultant Editor in A.M.Sci.
CRC-A.M. Advisor
NOVA MATH books ADVISOR
ganastss at memphis.edu<mailto:ganastss at memphis.edu>
http://www.eudoxuspress.com
http://www.msci.memphis.edu/~ganastss/jocaaa
http://www.msci.memphis.edu/~ganastss/jcaam
http://www.msci.memphis.edu/~ganastss/jafa
tel:(INT 001)- 901-678-3144 office
901-751-3553 home
901-678-2482 secr.
Fax: 901-678-2480
Associate Editor in:
J.Communications in Applied Analysis,
Inter.J.Applied Math.,Inter.J.Diff.Eq.&Appl.,CUBO,
J.Advances in non-linear Variational Inequalities,
e-J.of Inequalities in Pure and Applied Math.,
Anals U.Oradea-Fasciola Mathematica,
Journal of Inequalities and Applications,
Inter.J.of Pure&Appl.Math.,MIA,
Inter.J.of Computational and Numerical Analysis with Appl.
President of World Soc.for study & promotion of Ancient Greek Mathematics
Honorary Editor Australian Journal of Mathematical Analysis and Appl.
Panamerican Mathematical Journal
Eudoxus Press,LLC Pres.,ETC.
_______________________________________________
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Banach at math.okstate.edu
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From alspach at fourier.math.okstate.edu Sun Jan 20 07:54:46 2008
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id 98662D0999; Sun, 20 Jan 2008 07:54:46 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Gestur Olafsson and Boris Rubin
Message-Id: <20080120135446.98662D0999 at fourier.math.okstate.edu>
Date: Sun, 20 Jan 2008 07:54:46 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Invariant functions on
Grassmannians" by Gestur Olafsson and Boris Rubin.
Abstract: It is known, that every function on the unit sphere in
$\bbr^n$, which is invariant under rotations about some coordinate axis,
is completely determined by a function of one variable. Similar results,
when invariance of a function reduces dimension of its actual argument,
hold for every compact symmetric space and can be obtained in the
framework of Lie-theoretic consideration. In the present
article, this phenomenon is given precise meaning for functions on the
Grassmann manifold $G_{n,i}$ of $i$-dimensional
subspaces of $\bbr^n$, which are invariant under orthogonal
transformations preserving complementary coordinate subspaces of
arbitrary fixed dimension.
The corresponding integral formulas are obtained. Our method relies on
bi-Stiefel decomposition and does not invoke Lie theory.
Archive classification: math.FA
Mathematics Subject Classification: 44A12; 52A38
Remarks: 11 pages
The source file(s), GOBR_8_arxiv.tex: 39436 bytes, is(are) stored in
gzipped form as 0801.0081.gz with size 14kb. The corresponding postcript
file has gzipped size 89kb.
Submitted from: borisr at math.lsu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.0081
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http://arXiv.org/abs/0801.0081
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From alspach at fourier.math.okstate.edu Tue Jan 22 21:43:44 2008
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id 450DBD0A7E; Tue, 22 Jan 2008 21:43:44 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Sonja Cox and Mark Veraar
Message-Id: <20080123034344.450DBD0A7E at fourier.math.okstate.edu>
Date: Tue, 22 Jan 2008 21:43:44 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Some remarks on tangent martingale
difference sequences in $L^1$-spaces" by Sonja Cox and Mark Veraar.
Abstract: Let $X$ be a Banach space. Suppose that for all $p\in (1,
\infty)$ a constant $C_{p,X}$ depending only on $X$ and $p$ exists
such that for any two $X$-valued martingales $f$ and $g$ with tangent
martingale difference sequences one has \[\E\|f\|^p \leq C_{p,X}
\E\|g\|^p \ \ \ \ \ \ (*).\] This property is equivalent to the UMD
condition. In fact, it is still equivalent to the UMD condition if in
addition one demands that either $f$ or $g$ satisfy the so-called (CI)
condition. However, for some applications it suffices to assume that $(*)$
holds whenever $g$ satisfies the (CI) condition. We show that the class of
Banach spaces for which $(*)$ holds whenever only $g$ satisfies the (CI)
condition is more general than the class of UMD spaces, in particular
it includes the space $L^1$. We state several problems related to $(*)$
and other decoupling inequalities.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 60B05; 46B09; 60G42
Citation: Electron. Commun. Probab. 12, 421-433, (2007)
The source file(s), tangent_arxiv.tex: 47306 bytes, is(are) stored in
gzipped form as 0801.0695.gz with size 13kb. The corresponding postcript
file has gzipped size 101kb.
Submitted from: mark at profsonline.nl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.0695
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http://arXiv.org/abs/0801.0695
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From alspach at fourier.math.okstate.edu Tue Jan 22 21:48:39 2008
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id 5E4F8D0A7E; Tue, 22 Jan 2008 21:48:39 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Philippe Jaming, Mate Matolcsi, and Szilard Gy. Revesz
Message-Id: <20080123034839.5E4F8D0A7E at fourier.math.okstate.edu>
Date: Tue, 22 Jan 2008 21:48:39 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On the extremal rays of the
cone of positive, positive definite functions" by Philippe Jaming,
Mate Matolcsi, and Szilard Gy. Revesz.
Abstract: The aim of this paper is to investigate the cone
of non-negative, radial, positive-definite functions in the set of
continuous functions on $\R^d$. Elements of this cone admit a Choquet
integral representation in terms of the extremals. The main feature of
this article is to characterize some large classes of such extremals. In
particular, we show that there many other extremals than the gaussians,
thus disproving a conjecture of G. Choquet and that no reasonable
conjecture can be made on the full set of extremals. The last feature of
this article is to show that many characterizations of positive definite
functions available in the literature are actually particular cases of
the Choquet integral representations we obtain.
Archive classification: math.CA math.FA math.PR
Mathematics Subject Classification: 42A82
The source file(s), domain.eps: 12230 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.0941
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http://arXiv.org/abs/0801.0941
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From alspach at fourier.math.okstate.edu Wed Feb 6 08:33:39 2008
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id 80BB6D0991; Wed, 6 Feb 2008 08:33:39 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Romain Tessera
Message-Id: <20080206143339.80BB6D0991 at fourier.math.okstate.edu>
Date: Wed, 6 Feb 2008 08:33:39 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Finding left inverses for classes
of operators on l^p(Z^d) with some decay conditions" by Romain Tessera.
Abstract: We study the left-invertibility of infinite matrices indexed
by metric spaces with polynomial growth. In particular, we consider
matrices with polynomial decay, indexed by discrete groups of polynomial
growth. Under different conditions on the rows and the columns, we
prove that being bounded-below in l^p for some p implies that there is
a left-inverse which is bounded in l^q, for all q between 1 and infinity.
Archive classification: math.FA
Mathematics Subject Classification: 47B38, 47B37
Remarks: 33 pages
The source file(s), thinop10.tex: 77101 bytes, is(are) stored in gzipped
form as 0801.1532.gz with size 23kb. The corresponding postcript file
has gzipped size 163kb.
Submitted from: tessera at phare.normalesup.org
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.1532
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http://arXiv.org/abs/0801.1532
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From alspach at fourier.math.okstate.edu Wed Feb 6 08:35:34 2008
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id EDA12D0991; Wed, 6 Feb 2008 08:35:33 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by V. Valov
Message-Id: <20080206143533.EDA12D0991 at fourier.math.okstate.edu>
Date: Wed, 6 Feb 2008 08:35:33 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Probability measures and Milyutin
maps between metric spaces" by V. Valov.
Abstract: We prove that the functor $\Hat{P}$ of Radon probability
measures transforms any open map between completely metrizable spaces
into a soft map. This result is applied to establish some properties of
Milyutin maps between completely metrizable space.
Archive classification: math.GN math.FA
Mathematics Subject Classification: 54C60(primary), 60B05(secondary)
Remarks: 14 pages
The source file(s), Probability2.tex: 46900 bytes, is(are) stored in
gzipped form as 0801.1721.gz with size 14kb. The corresponding postcript
file has gzipped size 101kb.
Submitted from: veskov at nipissingu.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.1721
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http://arXiv.org/abs/0801.1721
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From alspach at fourier.math.okstate.edu Wed Feb 6 08:37:54 2008
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id 7185AD0991; Wed, 6 Feb 2008 08:37:54 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by G. Botelho, M. C. Matos and D. Pellegrino
Message-Id: <20080206143754.7185AD0991 at fourier.math.okstate.edu>
Date: Wed, 6 Feb 2008 08:37:54 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Lineability of summing sets of
homogeneous polynomials" by G. Botelho, M. C. Matos and D. Pellegrino.
Abstract: Given a continuous $n$-homogeneous polynomial $P\colon
E\longrightarrow F$ between Banach spaces and $1\leq q\leq p<\infty$,
in this paper we investigate some properties concerning lineability
and spaceability of the $(p;q)$-summing set of $P$, defined by
$S_{p;q}(P)=\{a\in E:P\mathrm{~is~}% (p;q)\mathrm{-summing~at~}a\}$.
Archive classification: math.FA
Mathematics Subject Classification: 46G25
Remarks: 15 pages
The source file(s), BotelhoMatosPellegrino.tex: 47676 bytes, is(are)
stored in gzipped form as 0801.1812.gz with size 14kb. The corresponding
postcript file has gzipped size 100kb.
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.1812
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http://arXiv.org/abs/0801.1812
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uget 0801.1812
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From alspach at fourier.math.okstate.edu Wed Feb 6 08:38:57 2008
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id 9BFF9D0991; Wed, 6 Feb 2008 08:38:57 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Marius Junge
Message-Id: <20080206143857.9BFF9D0991 at fourier.math.okstate.edu>
Date: Wed, 6 Feb 2008 08:38:57 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Noncommutative Riesz transforms
I-an algebraic approach" by Marius Junge.
Abstract: Riesz transforms on Rn or Riemanian manifolds are classical
examples of singular integrals. In this paper we consider Riesz transforms
associated to a semigroup Tt of completely positive trace preserving maps
on a finite von Neumann algebra. Given a generator A of the semigroup
we consider the square of the gradient
Gamma(x,y)=A(x^*y)-A(x^*)y-x^*A(y) We prove un upper bound
||\Gamma(x,x)^{1/2}\|_p \le c(p) || (-\Delta)^{1/2}x ||_p under suitable
assumptions. These estimates generalizes commutative results
by P.A. Meyer, Bakry, Emry, Gundy, Piser. Key tools are square function
inequalities obtained in joint work with C. Le Merdy and Q. Xu and
new algebraic relations. As an application we obtain new examples of
quantum metric spaces for discrete groups with the Haagerup property
and rapid decay.
Archive classification: math.OA math.FA
Mathematics Subject Classification: 46L25
The source file(s), mainfile2.tex: 192365 bytes, is(are) stored in gzipped
form as 0801.1873.gz with size 59kb. The corresponding postcript file
has gzipped size 283kb.
Submitted from: junge at math.uiuc.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.1873
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http://arXiv.org/abs/0801.1873
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From alspach at fourier.math.okstate.edu Wed Feb 6 08:49:46 2008
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To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Geraldo Botelho and Daniel Pellegrino
Message-Id: <20080206144946.7F4BFD0991 at fourier.math.okstate.edu>
Date: Wed, 6 Feb 2008 08:49:46 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Absolutely summing linear
operators into spaces with no finite cotype" by Geraldo Botelho and
Daniel Pellegrino.
Abstract: Given an infinite-dimensional Banach space $X$ and a Banach
space $Y$ with no finite cotype, we determine whether or not every
continuous linear operator from $X$ to $Y$ is absolutely $(q;p)$-summing
for almost all choices of $p$ and $q$, including the case $p=q$. If $X$
assumes its cotype, the problem is solved for all choices of $p$ and
$q$. Applications to the theory of dominated multilinear mappings are
also provided.
Archive classification: math.FA
Mathematics Subject Classification: 47B10
Remarks: 7 pages
The source file(s), Botelho-Pellegrino-BullPolish.tex: 22261 bytes,
is(are) stored in gzipped form as 0801.2051.gz with size 7kb. The
corresponding postcript file has gzipped size 74kb.
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.2051
or
http://arXiv.org/abs/0801.2051
or by email in unzipped form by transmitting an empty message with
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uget 0801.2051
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From alspach at fourier.math.okstate.edu Wed Feb 6 08:50:39 2008
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id BCCF3D0991; Wed, 6 Feb 2008 08:50:39 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jarno Talponen
Message-Id: <20080206145039.BCCF3D0991 at fourier.math.okstate.edu>
Date: Wed, 6 Feb 2008 08:50:39 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Operators on C_{0}(L,X) whose
range does not contain c_{0}" by Jarno Talponen.
Abstract: This paper contains the following results: a) Suppose that
X is a non-trivial Banach space and L is a non-empty locally compact
Hausdorff space without any isolated points. Then each linear operator
T: C_{0}(L,X)\to C_{0}(L,X), whose range does not contain C_{00}
isomorphically, satisfies the Daugavet equality ||I+T||=1+||T||. b)
Let \Gamma be a non-empty set and X, Y be Banach spaces such that X is
reflexive and Y does not contain c_{0} isomorphically. Then any continuous
linear operator T: c_{0}(\Gamma,X)\to Y is weakly compact.
Archive classification: math.FA
Mathematics Subject Classification: 46B20; 46B28
The source file(s), dgvt_talponen.tex: 17582 bytes, is(are) stored in
gzipped form as 0801.2314.gz with size 6kb. The corresponding postcript
file has gzipped size 61kb.
Submitted from: talponen at cc.helsinki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.2314
or
http://arXiv.org/abs/0801.2314
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From alspach at fourier.math.okstate.edu Wed Feb 6 08:51:36 2008
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id 00948D0991; Wed, 6 Feb 2008 08:51:35 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jarno Talponen
Message-Id: <20080206145136.00948D0991 at fourier.math.okstate.edu>
Date: Wed, 6 Feb 2008 08:51:35 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A note on the class of super
reflexive almost transitive Banach spaces" by Jarno Talponen.
Abstract: The class J of simultaneously almost transitive, uniformly
convex and uniformly smooth Banach spaces is characterized in terms of
convex-transitivity and weak geometry of the norm.
Archive classification: math.FA
Mathematics Subject Classification: 46B04; 46B20
The source file(s), NoteJ.tex: 21992 bytes, is(are) stored in gzipped
form as 0801.2320.gz with size 8kb. The corresponding postcript file
has gzipped size 57kb.
Submitted from: talponen at cc.helsinki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.2320
or
http://arXiv.org/abs/0801.2320
or by email in unzipped form by transmitting an empty message with
subject line
uget 0801.2320
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to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Feb 19 09:25:17 2008
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id 1AFA4D09FA; Tue, 19 Feb 2008 09:25:17 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Yves Dutrieux Gilles Lancien
Message-Id: <20080219152517.1AFA4D09FA at fourier.math.okstate.edu>
Date: Tue, 19 Feb 2008 09:25:17 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Isometric embeddings of compact
spaces into Banach spaces" by Yves Dutrieux Gilles Lancien.
Abstract: We show the existence of a compact metric space $K$ such that
whenever $K$ embeds isometrically into a Banach space $Y$, then any
separable Banach space is linearly isometric to a subspace of $Y$. We
also address the following related question: if a Banach space $Y$
contains an isometric copy of the unit ball or of some special compact
subset of a separable Banach space $X$, does it necessarily contain a
subspace isometric to $X$? We answer positively this question when $X$
is a polyhedral finite-dimensional space, $c_0$ or $\ell_1$.
Archive classification: math.FA
Mathematics Subject Classification: 46B04; 46B20
Remarks: 8 pages
The source file(s), dutrieux_lancien.tex: 22590 bytes, is(are) stored in
gzipped form as 0801.2486.gz with size 8kb. The corresponding postcript
file has gzipped size 79kb.
Submitted from: gilles.lancien at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.2486
or
http://arXiv.org/abs/0801.2486
or by email in unzipped form by transmitting an empty message with
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uget 0801.2486
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From alspach at fourier.math.okstate.edu Tue Feb 19 09:30:57 2008
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id 14A39D09FA; Tue, 19 Feb 2008 09:30:56 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jesus Araujo and Juan J. Font
Message-Id: <20080219153057.14A39D09FA at fourier.math.okstate.edu>
Date: Tue, 19 Feb 2008 09:30:56 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Stability and instability of
weighted composition operators" by Jesus Araujo and Juan J. Font.
Abstract: Let $\epsilon >0$. A continuous linear operator
$T:C(X) \ra C(Y)$ is said to be {\em $\epsilon$-disjointness preserving}
if $\vc (Tf)(Tg)\vd_{\infty} \le \epsilon$, whenever $f,g\in C(X)$ satisfy
$\vc f\vd_{\infty} =\vc g\vd_{\infty} =1$ and $fg\equiv 0$. In this
paper we address basically two main questions:
1.- How close there must be a weighted composition operator to a given
$\epsilon$-disjointness preserving operator?
2.- How far can the set of weighted composition operators be from
a given $\epsilon$-disjointness preserving operator?
We address these two questions distinguishing among three cases: $X$
infinite, $X$ finite, and $Y$ a singleton ($\epsilon$-disjointness
preserving functionals).
We provide sharp stability and instability bounds for the three cases.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47B38; Secondary 46J10, 47B33
Remarks: 37 pages, 7 figures. A beamer presentation at www.araujo.tk
The source file(s), ejemploy0d.eps: 10802 bytes stability86.tex: 91977
bytes total2gabove.eps: 20323 bytes total2i.eps: 20467 bytes w01c.eps:
9921 bytes w11d.eps: 12594 bytes w21d.eps: 12278 bytes z1d.eps: 12984
bytes, is(are) stored in gzipped form as 0801.2532.tar.gz with size
46kb. The corresponding postcript file has gzipped size 180kb.
Submitted from: araujoj at unican.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.2532
or
http://arXiv.org/abs/0801.2532
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From alspach at fourier.math.okstate.edu Tue Feb 19 09:32:56 2008
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id 9327AD09FA; Tue, 19 Feb 2008 09:32:56 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by O. Hirzallah, F. Kittaneh, and M. S. Moslehian
Message-Id: <20080219153256.9327AD09FA at fourier.math.okstate.edu>
Date: Tue, 19 Feb 2008 09:32:56 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Schatten p-norm inequalities
related to a characterization of inner product spaces" by O. Hirzallah,
F. Kittaneh, and M. S. Moslehian.
Abstract: Let $A_1, \cdots A_n$ be operators acting on a separable
complex Hilbert space such that $\sum_{i=1}^n A_i=0$. It is shown that
if $A_1, \cdots A_n$ belong to a Schatten $p$-class, for some $p>0$,
then \begin{equation*} 2^{p/2}n^{p-1} \sum_{i=1}^n \|A_i\|^p_p \leq
\sum_{i,j=1}^n\|A_i\pm A_j\|^p_p \end{equation*} for $0<p\leq 2$, and the
reverse inequality holds for $2\leq p<\infty$. Moreover, \begin{equation*}
\sum_{i,j=1}^n\|A_i\pm A_j\|^2_p \leq 2n^{2/p} \sum_{i=1}^n \|A_i\|^2_p
\end{equation*} for $0<p\leq 2$, and the reverse inequality holds for
$2\leq p<\infty$. These inequalities are related to a characterization
of inner product spaces due to E.R. Lorch.
Archive classification: math.OA math.FA
Mathematics Subject Classification: 46C15, 47A30, 47B10, 47B15
Remarks: 6 pages
The source file(s),
Schattenp-norminequalitiesrelatedtoacharacteriztionofinnerproductspaces.tex:
14968 bytes, is(are) stored in gzipped form as 0801.2726.gz with size
4kb. The corresponding postcript file has gzipped size 56kb.
Submitted from: moslehian at ferdowsi.um.ac.ir
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.2726
or
http://arXiv.org/abs/0801.2726
or by email in unzipped form by transmitting an empty message with
subject line
uget 0801.2726
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From alspach at fourier.math.okstate.edu Tue Feb 19 09:34:07 2008
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X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id EED7DD09FA; Tue, 19 Feb 2008 09:34:07 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by A. Ibort, P. Linares, and J. G. Llavona
Message-Id: <20080219153407.EED7DD09FA at fourier.math.okstate.edu>
Date: Tue, 19 Feb 2008 09:34:07 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Continuous multilinear functionals
on $C(K)$-spaces are integral" by A. Ibort, P. Linares, and J. G. Llavona.
Abstract: In this paper we prove the theorem stated on the title:
every continuous multilinear functional on $C(K)$-spaces is integral,
or what is the same any polymeasure defined on the product of Borelian
$\sigma$-algebras defined on compact sets can be extended to a bounded
Borel measure on the compact product space. We provide two different
proofs of the same result, each one stressing a different aspect of the
various implications of this fact. The first one, valid for compact
subsets of $\R^n$, is based on the classical multivariate theory of
moments and is a natural extension of the Hausdorff moment problem
to multilinear functionals. The second proof relies on a multilinear
extension of the decomposition theorem of linear functionals on its
positive and negative part which allows us prove a multilinear Riesz
Theorem as well. These arguments are valid for arbitrary Hausdorff
compact sets.
Archive classification: math.FA
Mathematics Subject Classification: 46G25
Remarks: 10 pages
The source file(s), Integralmultilinear.tex: 39365 bytes, is(are)
stored in gzipped form as 0801.2878.gz with size 13kb. The corresponding
postcript file has gzipped size 85kb.
Submitted from: plinares at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.2878
or
http://arXiv.org/abs/0801.2878
or by email in unzipped form by transmitting an empty message with
subject line
uget 0801.2878
or in gzipped form by using subject line
get 0801.2878
to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Feb 19 09:35:55 2008
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id D7456D09FA; Tue, 19 Feb 2008 09:35:55 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Olivier Guedon, Shahar Mendelson, Alain Pajor, and Nicole Tomczak-Jaegermann
Message-Id: <20080219153555.D7456D09FA at fourier.math.okstate.edu>
Date: Tue, 19 Feb 2008 09:35:55 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Majorizing measures and
proportional subsets of bounded orthonormal systems" by Olivier Guedon,
Shahar Mendelson, Alain Pajor, and Nicole Tomczak-Jaegermann.
Abstract: In this article we prove that for any orthonormal system
$(\vphi_j)_{j=1}^n \subset L_2$ that is bounded in $L_{\infty}$, and any
$1 < k <n$, there exists a subset $I$ of cardinality greater than $n-k$
such that on $\spa\{\vphi_i\}_{i \in I}$, the $L_1$ norm and the $L_2$
norm are equivalent up to a factor $\mu (\log \mu)^{5/2}$, where $\mu =
\sqrt{n/k} \sqrt{\log k}$. The proof is based on a new estimate of the
supremum of an empirical process on the unit ball of a Banach space with
a good modulus of convexity, via the use of majorizing measures.
Archive classification: math.FA math.PR
The source file(s), arXiv.tex: 50357 bytes, is(are) stored in gzipped
form as 0801.3556.gz with size 16kb. The corresponding postcript file
has gzipped size 130kb.
Submitted from: alain.pajor at univ-mlv.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.3556
or
http://arXiv.org/abs/0801.3556
or by email in unzipped form by transmitting an empty message with
subject line
uget 0801.3556
or in gzipped form by using subject line
get 0801.3556
to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Feb 19 09:32:56 2008
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
Delivered-To: alspach at fourier.math.okstate.edu
Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 9327AD09FA; Tue, 19 Feb 2008 09:32:56 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by O. Hirzallah, F. Kittaneh, and M. S. Moslehian
Message-Id: <20080219153256.9327AD09FA at fourier.math.okstate.edu>
Date: Tue, 19 Feb 2008 09:32:56 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Schatten p-norm inequalities
related to a characterization of inner product spaces" by O. Hirzallah,
F. Kittaneh, and M. S. Moslehian.
Abstract: Let $A_1, \cdots A_n$ be operators acting on a separable
complex Hilbert space such that $\sum_{i=1}^n A_i=0$. It is shown that
if $A_1, \cdots A_n$ belong to a Schatten $p$-class, for some $p>0$,
then \begin{equation*} 2^{p/2}n^{p-1} \sum_{i=1}^n \|A_i\|^p_p \leq
\sum_{i,j=1}^n\|A_i\pm A_j\|^p_p \end{equation*} for $0<p\leq 2$, and the
reverse inequality holds for $2\leq p<\infty$. Moreover, \begin{equation*}
\sum_{i,j=1}^n\|A_i\pm A_j\|^2_p \leq 2n^{2/p} \sum_{i=1}^n \|A_i\|^2_p
\end{equation*} for $0<p\leq 2$, and the reverse inequality holds for
$2\leq p<\infty$. These inequalities are related to a characterization
of inner product spaces due to E.R. Lorch.
Archive classification: math.OA math.FA
Mathematics Subject Classification: 46C15, 47A30, 47B10, 47B15
Remarks: 6 pages
The source file(s),
Schattenp-norminequalitiesrelatedtoacharacteriztionofinnerproductspaces.tex:
14968 bytes, is(are) stored in gzipped form as 0801.2726.gz with size
4kb. The corresponding postcript file has gzipped size 56kb.
Submitted from: moslehian at ferdowsi.um.ac.ir
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.2726
or
http://arXiv.org/abs/0801.2726
or by email in unzipped form by transmitting an empty message with
subject line
uget 0801.2726
or in gzipped form by using subject line
get 0801.2726
to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Feb 19 09:34:07 2008
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
Delivered-To: alspach at fourier.math.okstate.edu
Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id EED7DD09FA; Tue, 19 Feb 2008 09:34:07 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by A. Ibort, P. Linares, and J. G. Llavona
Message-Id: <20080219153407.EED7DD09FA at fourier.math.okstate.edu>
Date: Tue, 19 Feb 2008 09:34:07 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Continuous multilinear functionals
on $C(K)$-spaces are integral" by A. Ibort, P. Linares, and J. G. Llavona.
Abstract: In this paper we prove the theorem stated on the title:
every continuous multilinear functional on $C(K)$-spaces is integral,
or what is the same any polymeasure defined on the product of Borelian
$\sigma$-algebras defined on compact sets can be extended to a bounded
Borel measure on the compact product space. We provide two different
proofs of the same result, each one stressing a different aspect of the
various implications of this fact. The first one, valid for compact
subsets of $\R^n$, is based on the classical multivariate theory of
moments and is a natural extension of the Hausdorff moment problem
to multilinear functionals. The second proof relies on a multilinear
extension of the decomposition theorem of linear functionals on its
positive and negative part which allows us prove a multilinear Riesz
Theorem as well. These arguments are valid for arbitrary Hausdorff
compact sets.
Archive classification: math.FA
Mathematics Subject Classification: 46G25
Remarks: 10 pages
The source file(s), Integralmultilinear.tex: 39365 bytes, is(are)
stored in gzipped form as 0801.2878.gz with size 13kb. The corresponding
postcript file has gzipped size 85kb.
Submitted from: plinares at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.2878
or
http://arXiv.org/abs/0801.2878
or by email in unzipped form by transmitting an empty message with
subject line
uget 0801.2878
or in gzipped form by using subject line
get 0801.2878
to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Feb 19 09:35:55 2008
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
Delivered-To: alspach at fourier.math.okstate.edu
Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id D7456D09FA; Tue, 19 Feb 2008 09:35:55 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Olivier Guedon, Shahar Mendelson, Alain Pajor, and Nicole Tomczak-Jaegermann
Message-Id: <20080219153555.D7456D09FA at fourier.math.okstate.edu>
Date: Tue, 19 Feb 2008 09:35:55 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Majorizing measures and
proportional subsets of bounded orthonormal systems" by Olivier Guedon,
Shahar Mendelson, Alain Pajor, and Nicole Tomczak-Jaegermann.
Abstract: In this article we prove that for any orthonormal system
$(\vphi_j)_{j=1}^n \subset L_2$ that is bounded in $L_{\infty}$, and any
$1 < k <n$, there exists a subset $I$ of cardinality greater than $n-k$
such that on $\spa\{\vphi_i\}_{i \in I}$, the $L_1$ norm and the $L_2$
norm are equivalent up to a factor $\mu (\log \mu)^{5/2}$, where $\mu =
\sqrt{n/k} \sqrt{\log k}$. The proof is based on a new estimate of the
supremum of an empirical process on the unit ball of a Banach space with
a good modulus of convexity, via the use of majorizing measures.
Archive classification: math.FA math.PR
The source file(s), arXiv.tex: 50357 bytes, is(are) stored in gzipped
form as 0801.3556.gz with size 16kb. The corresponding postcript file
has gzipped size 130kb.
Submitted from: alain.pajor at univ-mlv.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0801.3556
or
http://arXiv.org/abs/0801.3556
or by email in unzipped form by transmitting an empty message with
subject line
uget 0801.3556
or in gzipped form by using subject line
get 0801.3556
to: math at arXiv.org.
From banach-bounces at math.okstate.edu Tue Jan 29 10:23:24 2008
Return-Path: <banach-bounces at math.okstate.edu>
Message-Id: <a06230900c3c4f77899e0 at [129.22.117.91]>
Date: Tue, 29 Jan 2008 10:40:53 -0500
To: banach at math.okstate.edu
From: "Stanislaw J. Szarek" <szarek at cwru.edu>
Subject: [Banach] Postdoctoral position at Case Western Reserve University
Department of Mathematics at Case Western Reserve University
invites applications for a post-doctoral position starting in the
fall of 2008. The position is funded by the NSF Focused Research
Group grant "Collaborative Research: Fourier analytic and
probabilistic methods in geometric functional analysis and convexity"
(see http://www.math.ucdavis.edu/~geofunction).
We seek applicants in the area of functional analysis, convexity
theory and related high-dimensional phenomena, the direction that
recently has been often referred to as ``asymptotic geometric
analysis" and of which members of the Department are internationally
recognized leaders. See http://www.cwru.edu/artsci/math/szarek/ and
http://www.cwru.edu/artsci/math/werner/ for examples of recent
research directions. The starting date of the appointment is
somewhat flexible, as is the profile: it may involve either 100%
effort commitment to the grant (no teaching duties), or an effort
split between the grant and teaching (see
http://www.case.edu/artsci/math/employment.htm under "Other
Searches: Mathematics: Lecturer"). The appointment is initially
budgeted for one year, but longer durations under the split effort
scenario may be considered.
Applicants should submit a letter of application, AMS cover sheet,
CV, and have three letters of evaluation sent, preferably by email to
math-faculty-position at cwru.edu, with copies to szarek at cwru.edu and
elisabeth.werner at case.edu. Applications received by February 15,
2008 will receive full consideration; applications will be accepted
until the position is filled.
Case is an integral part of one of the major research medical
complexes in the country. It also has a major presence in various
science and engineering disciplines. Geographically, it is located
on the eastern edge of Cleveland, in northeast Ohio, adjacent to
University Circle, home to the Cleveland Symphony Orchestra, the
Cleveland Museum of Art, and many other cultural institutions. There
is a wide variety of housing, schooling, and other amenities nearby.
Case Western Reserve University is committed to diversity and is
an affirmative action, equal opportunity employer. Applications from
women or minorities are especially encouraged.
_______________________________________________
Banach mailing list
Banach at math.okstate.edu
http://hardy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Tue Feb 19 10:06:02 2008
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id 8AB42D09FA; Tue, 19 Feb 2008 10:06:02 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Gilles Pisier
Message-Id: <20080219160602.8AB42D09FA at fourier.math.okstate.edu>
Date: Tue, 19 Feb 2008 10:06:02 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Complex interpolation between
Hilbert, Banach and operator spaces" by Gilles Pisier.
Abstract: Motivated by a question of Vincent Lafforgue, we study
the Banach spaces $X$ satisfying the following property:\ there is
a function $\vp\to \Delta_X(\vp)$ tending to zero with $\vp>0$ such
that every operator $T\colon \ L_2\to L_2$ with $\|T\|\le \vp$ that
is simultaneously contractive (i.e.\ of norm $\le 1$) on $L_1$ and on
$L_\infty$ must be of norm $\le \Delta_X(\vp)$ on $L_2(X)$.
We show that $\Delta_X(\vp)\in O(\vp^\alpha)$ for some $\alpha>0$
iff $X$ is isomorphic to a quotient of a subspace of an ultraproduct of
$\theta$-Hilbertian spaces for some $ \theta>0$ (see Corollary
\ref{comcor4.3}), where $\theta$-Hilbertian is meant in a slightly
more general sense than in our previous paper \cite{P1}. Let
$B_{{r}}(L_2(\mu))$ be the space of all regular operators on
$L_2(\mu)$. We are able to describe the complex interpolation space \[
(B_{{r}}(L_2(\mu), B(L_2(\mu))^\theta. \] We show that $T\colon \
L_2(\mu)\to L_2(\mu)$ belongs to this space iff $T\otimes id_X$ is
bounded on $L_2(X)$ for any $\theta$-Hilbertian space $X$.
More generally, we are able to describe the spaces $$ (B(\ell_{p_0}),
B(\ell_{p_1}))^\theta \ {\rm or}\ (B(L_{p_0}), B(L_{p_1}))^\theta $$ for
any pair $1\le p_0,p_1\le \infty$ and $0<\theta<1$. In the same vein,
given a locally compact Abelian group $G$, let $M(G)$ (resp.\ $PM(G)$)
be the space of complex measures (resp.\ pseudo-measures) on $G$ equipped
with the usual norm $\|\mu\|_{M(G)} = |\mu|(G)$ (resp. \[ \|\mu\|_{PM(G)}
= \sup\{|\hat\mu(\gamma)| \ \big| \ \gamma\in\widehat G\}). \] We describe
similarly the interpolation space $(M(G), PM(G))^\theta$. Various
extensions and variants of this result will be given, e.g.\ to Schur
multipliers on $B(\ell_2)$ and to operator spaces.
Archive classification: math.FA math.OA
The source file(s), complex.4fev08.tex: 174268 bytes, is(are) stored in
gzipped form as 0802.0476.gz with size 51kb. The corresponding postcript
file has gzipped size 253kb.
Submitted from: pisier at math.jussieu.fr
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From alspach at fourier.math.okstate.edu Fri Feb 22 11:23:07 2008
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id 25B3AD0A6B; Fri, 22 Feb 2008 11:23:07 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Matthew Neal and Bernard Russo
Message-Id: <20080222172307.25B3AD0A6B at fourier.math.okstate.edu>
Date: Fri, 22 Feb 2008 11:23:07 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Contractively complemented
subspaces of pre-symmetric spaces" by Matthew Neal and Bernard Russo.
Abstract: In 1965, Ron Douglas proved that if $X$ is a closed subspace
of an $L^1$-space and $X$ is isometric to another $L^1$-space, then $X$
is the range of a contractive projection on the containing $L^1$-space. In
1977 Arazy-Friedman showed that if a subspace $X$ of $C_1$ is isometric
to another $C_1$-space (possibly finite dimensional), then there is
a contractive projection of $C_1$ onto $X$. In 1993 Kirchberg proved
that if a subspace $X$ of the predual of a von Neumann algebra $M$ is
isometric to the predual of another von Neumann algebra, then there is
a contractive projection of the predual of $M$ onto $X$.
We widen significantly the scope of these results by showing that if a
subspace $X$ of the predual of a $JBW^*$-triple $A$ is isometric to
the predual of another $JBW^*$-triple $B$, then there is a contractive
projection on the predual of $A$ with range $X$, as long as $B$ does
not have a direct summand which is isometric to a space of the form
$L^\infty(\Omega,H)$, where $H$ is a Hilbert space of dimension at least
two. The result is false without this restriction on $B$.
Archive classification: math.OA math.FA
Mathematics Subject Classification: 46B04,46L70,17C65
Remarks: 25 pages
The source file(s), ngoz020508.tex: 97855 bytes, is(are) stored in gzipped
form as 0802.0734.gz with size 29kb. The corresponding postcript file
has gzipped size 155kb.
Submitted from: brusso at math.uci.edu
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From alspach at fourier.math.okstate.edu Fri Feb 22 11:24:29 2008
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id B5454D0A6B; Fri, 22 Feb 2008 11:24:29 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Wieslaw Kubis
Message-Id: <20080222172429.B5454D0A6B at fourier.math.okstate.edu>
Date: Fri, 22 Feb 2008 11:24:29 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Banach spaces with projectional
skeletons" by Wieslaw Kubis.
Abstract: A projectional skeleton in a Banach space is a sigma-directed
family of projections onto separable subspaces, covering the entire
space. The class of Banach spaces with projectional skeletons is strictly
larger than the class of Plichko spaces (i.e. Banach spaces with a
countably norming Markushevich basis). We show that every space with
a projectional skeleton has a projectional resolution of the identity
and has a norming space with similar properties to Sigma-spaces. We
characterize the existence of a projectional skeleton in terms of
elementary substructures, providing simple proofs of known results
concerning weakly compactly generated spaces and Plichko spaces.
We prove a preservation result for Plichko Banach spaces, involving
transfinite sequences of projections. As a corollary, we show that a
Banach space is Plichko if and only if it has a commutative projectional
skeleton.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 46B26; 46B03; 46E15; 54C35
Remarks: 30 pages (including index and toc), submitted
The source file(s), projs_survey-ver2e.bbl: 7090 bytes
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From alspach at fourier.math.okstate.edu Fri Feb 22 11:27:33 2008
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id 6D462D0A6B; Fri, 22 Feb 2008 11:27:33 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by D.Karayannakis
Message-Id: <20080222172733.6D462D0A6B at fourier.math.okstate.edu>
Date: Fri, 22 Feb 2008 11:27:33 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On a conjectured inequality in
convex analysis in the case of the unit ball of lp^n" by D.Karayannakis.
Abstract: We re-confirm one of the recently stated conjectures of
G.Kuperberg of significant convex analysis interest and confirmed very
recently for the case of the unit p-ball by A.D.Gutierrez(by use of
polygamma functions and convexity theory),this time using only the
fundamentals of the gamma function and some mild classical analysis tools.
Archive classification: math.CA math.FA
Remarks: 4 pages,part of these results comprise a poster to be presented
at the 5th Congress of European Mathematics, Amsterdam July 2008
The source file(s), ONACONJECTUREDINEQUALITYINCONVEXANALYSISFORTHECA.pdf:
77405 bytes, is(are) stored in gzipped form as 0802.1942.pdf with size
76kb.
Submitted from: dkar at stef.teiher.gr
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http://front.math.ucdavis.edu/0802.1942
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http://arXiv.org/abs/0802.1942
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From alspach at fourier.math.okstate.edu Fri Feb 22 11:28:22 2008
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id C5DEED0A6B; Fri, 22 Feb 2008 11:28:22 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Heinz H. Bauschke, Xianfu Wang, Jane Ye and Xiaoming Yuan
Message-Id: <20080222172822.C5DEED0A6B at fourier.math.okstate.edu>
Date: Fri, 22 Feb 2008 11:28:22 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Bregman distances and Klee sets"
by Heinz H. Bauschke, Xianfu Wang, Jane Ye and Xiaoming Yuan.
Abstract: In 1960, Klee showed that a subset of a Euclidean space must be
a singleton provided that each point in the space has a unique farthest
point in the set. This classical result has received much attention; in
fact, the Hilbert space version is a famous open problem. In this paper,
we consider Klee sets from a new perspective. Rather than measuring
distance induced by a norm, we focus on the case when distance is meant
in the sense of Bregman, i.e., induced by a convex function. When the
convex function has sufficiently nice properties, then - analogously to
the Euclidean distance case - every Klee set must be a singleton. We
provide two proofs of this result, based on Monotone Operator Theory
and on Nonsmooth Analysis. The latter approach leads to results that
complement work by Hiriart-Urruty on the Euclidean case.
Archive classification: math.FA math.OC
Mathematics Subject Classification: 47H05; 41A65; 49J52
The source file(s), submitted.tex: 49600 bytes, is(are) stored in gzipped
form as 0802.2322.gz with size 15kb. The corresponding postcript file
has gzipped size 113kb.
Submitted from: heinz.bauschke at ubc.ca
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http://front.math.ucdavis.edu/0802.2322
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From alspach at fourier.math.okstate.edu Tue Feb 26 08:06:29 2008
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id 82B3ED0A4A; Tue, 26 Feb 2008 08:06:29 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Yoshimichi Ueda
Message-Id: <20080226140629.82B3ED0A4A at fourier.math.okstate.edu>
Date: Tue, 26 Feb 2008 08:06:29 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On peak phenomena for
non-commutative $H^\infty$" by Yoshimichi Ueda.
Abstract: A non-commutative extension of Amar and Lederer's peak
set result is given. As its simple applications it is shown that
any non-commutative $H^\infty$-algebra $H^\infty(M,\tau)$ has unique
predual, and moreover some of the results of Blecher and Labuschagne
are generalized to the complete form.
Archive classification: math.FA math.OA
The source file(s), peak.tex: 31983 bytes, is(are) stored in gzipped
form as 0802.3449.gz with size 10kb. The corresponding postcript file
has gzipped size 78kb.
Submitted from: ueda at math.kyushu-u.ac.jp
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http://front.math.ucdavis.edu/0802.3449
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From alspach at fourier.math.okstate.edu Wed Feb 27 09:46:44 2008
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id 1DDF9D0A7A; Wed, 27 Feb 2008 09:46:44 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Michael Cwikel
Message-Id: <20080227154644.1DDF9D0A7A at fourier.math.okstate.edu>
Date: Wed, 27 Feb 2008 09:46:44 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Complex interpolation of compact
operators mapping into lattice couples" by Michael Cwikel.
Abstract: Suppose that (A_0,A_1) and (B_0,B_1) are Banach couples, and
that T is a linear operator which maps A_0 compactly into B_0 and A_1
boundedly (or even compactly) into B_1.
Does this imply that T maps [A_0,A_1]_s to [B_0,B_1]_s compactly for
0<s<1 ? (Here, as usual, [A_0,A_1]_s denotes the complex interpolation
space of Alberto Calderon.)
This question has been open for 44 years. Affirmative answers are
known for it in many special cases. We answer it affirmatively in the
case where (A_0,A_1) is arbitrary and (B_0,B_1) is a couple of Banach
lattices having absolutely continuous norms or the Fatou property.
Archive classification: math.FA
Mathematics Subject Classification: 46B70, 46E30 (primary)
Remarks: 14 pages. (Page 13 contains routine and standard material
which you
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0802.3520
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From alspach at fourier.math.okstate.edu Wed Feb 27 09:48:17 2008
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id 72A4BD0A7A; Wed, 27 Feb 2008 09:48:17 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Peng Gao
Message-Id: <20080227154817.72A4BD0A7A at fourier.math.okstate.edu>
Date: Wed, 27 Feb 2008 09:48:17 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On $l^2$ norms of some weighted
mean matrices" by Peng Gao.
Abstract: We give another proof of a result of Bennett on the $l^{p}$
operator norms of some weighted mean matrices for the case $p=2$.
Archive classification: math.FA
Mathematics Subject Classification: 47A30
Remarks: 6 pages
The source file(s), Bilinearineqarxiv.tex: 25253 bytes, is(are) stored in
gzipped form as 0802.3546.gz with size 7kb. The corresponding postcript
file has gzipped size 71kb.
Submitted from: penggao at utsc.utoronto.ca
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From alspach at fourier.math.okstate.edu Wed Feb 27 09:49:09 2008
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id 48209D0A7A; Wed, 27 Feb 2008 09:49:09 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by M.I. Ostrovskii
Message-Id: <20080227154909.48209D0A7A at fourier.math.okstate.edu>
Date: Wed, 27 Feb 2008 09:49:09 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Coarse embeddability into Banach
spaces" by M.I. Ostrovskii.
Abstract: The main purposes of this paper are (1) To survey the area
of coarse embeddability of metric spaces into Banach spaces, and,
in particular, coarse embeddability of different Banach spaces into
each other; (2) To present new results on the problems: (a) Whether
coarse non-embeddability into $\ell_2$ implies presence of expander-like
structures? (b) To what extent $\ell_2$ is the most difficult space to
embed into?
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B20; 54E40
Remarks: 23 pages
The source file(s), Coarse2007.tex: 46609 bytes, is(are) stored in gzipped
form as 0802.3666.gz with size 15kb. The corresponding postcript file
has gzipped size 125kb.
Submitted from: ostrovsm at stjohns.edu
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http://front.math.ucdavis.edu/0802.3666
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From banach-bounces at math.okstate.edu Mon Feb 25 17:13:47 2008
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To: banach at math.okstate.edu
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Date: Mon, 25 Feb 2008 17:11:51 -0600
From: Dale Alspach <alspach at math.okstate.edu>
Subject: [Banach] Lior Tzafriri
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Lior Tzafriri, Professor Emeritus at the Hebrew University of Jerusalem,
died Sunday morning after undergoing heart surgery. Lior had recovered
from surgery he underwent in the autumn. He was leading a normal life,
going out, frequently coming to the
Institute of Mathematics, and was as well humored as usual.
Those who knew Lior will miss not only his sharp mathematical insights
but his enormous sense of humor, true wisdom, and his gentle behavior
that was so surprising for a person with such a strong personality and
independence of mind.
Lior's funeral will take place 12:00 Tuesday, February 26, at Bet
Hahesped,
We are very sorry to announce that Professor Lior Tzafriri passed away on
February 24, 2008. He died in Jerusalem during an open heart surgery
for replacement of a valve in his heart.
Lior was born on May 9, 1936 in Bucharest and emigrated to Israel in
1961. He started his university studies in Bucharest but did his PhD
in Jerusalem on the subject of spectral operators. He was on the
faculty of the Hebrew University since 1970, as a full professor since
1978. He was a visiting professor in several universities, including
Northwestern University, University of Minnesota, California Institute
of Technology, Cambridge University, University of Copenhagen, IHES,
Ohio State University and Texas A&M.
Most of his research work was in Banach space theory. Here are some
of his contributions to the subject:
1. The solution of the complemented subspaces problem (with
J. Lindenstrauss).
2. The structure theory of Orlicz sequence spaces (with
J. Lindenstrauss).
3. Spaces with unique unconditional bases up to permutation (with
J. Bourgain, P. Casazza and J. Lindenstrauss).
4. The textbooks: Classical Banach Spaces I, II (with
J. Lindenstrauss).
5. The 0-2 law (with Y. Katznelson).
6. The structure of Banach spaces with a symmetric structure (with
W. B. Johnson, B. Maurey and G. Schechtman).
7. Invertibility of large submatrices (with J. Bourgain).
8. The structure of finite dimensional subspaces of Lp (with
J. Bourgain).
9. Work on the Kadison Singer problem (with J. Bourgain).
Lior Tzafriri did an outstanding job as the chairman of the
Mathematics Department of the Hebrew University during his two separate
terms.
Those who knew Lior will miss not only his sharp mathematical insights
but his enormous sense of humor, true wisdom, and his gentle behavior
that was so surprising for a person with such a strong personality and
independence of mind.
Lior is survived by Marianna, his wife of 51 years;
his daughter Edna; his son Rami; and three grandchildren.
(Sent by Bill Johnson)
_______________________________________________
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From alspach at fourier.math.okstate.edu Fri Feb 29 15:01:17 2008
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id ACA05D09A1; Fri, 29 Feb 2008 15:01:17 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Mark Rudelson and Roman Vershynin
Message-Id: <20080229210117.ACA05D09A1 at fourier.math.okstate.edu>
Date: Fri, 29 Feb 2008 15:01:17 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The smallest singular value of
a random rectangular matrix" by Mark Rudelson and Roman Vershynin.
Abstract: We prove an optimal estimate on the smallest singular value of
a random subgaussian matrix, valid for all fixed dimensions. For an N by n
matrix A with independent and identically distributed subgaussian entries,
the smallest singular value of A is at least of the order \sqrt{N} -
\sqrt{n-1} with high probability. A sharp estimate on the probability
is also obtained.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 15A52, 11P70
Remarks: 32 pages
The source file(s), rv-rectangular-matrices.tex: 80875 bytes, is(are)
stored in gzipped form as 0802.3956.gz with size 23kb. The corresponding
postcript file has gzipped size 149kb.
Submitted from: rudelson at math.missouri.edu
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http://front.math.ucdavis.edu/0802.3956
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From alspach at fourier.math.okstate.edu Tue Mar 4 15:24:44 2008
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id 4D685D0A8A; Tue, 4 Mar 2008 15:24:44 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Yun-Su Kim
Message-Id: <20080304212444.4D685D0A8A at fourier.math.okstate.edu>
Date: Tue, 4 Mar 2008 15:24:44 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Banach Spaces with respect to
operator-valued norms" by Yun-Su Kim.
Abstract: We introduce the notions of L(H)-valued norms and Banach
spaces with respect to L(H)-valued norms. In particular, we introduce
Hilbert spaces with respect to L(H)-valued inner products. In addition,
we provide several fundamental examples of Hilbert spaces with respect
to L(H)-valued inner products.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 46B45 ; 46C07
Remarks: 13 page
The source file(s), 2o-Banach.tex: 41954 bytes, is(are) stored in gzipped
form as 0803.0041.gz with size 10kb. The corresponding postcript file
has gzipped size 83kb.
Submitted from: kimys at indiana.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0803.0041
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http://arXiv.org/abs/0803.0041
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From alspach at fourier.math.okstate.edu Wed Mar 5 11:59:54 2008
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id A349BD0A94; Wed, 5 Mar 2008 11:59:54 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jakub Onufry Wojtaszczyk
Message-Id: <20080305175954.A349BD0A94 at fourier.math.okstate.edu>
Date: Wed, 5 Mar 2008 11:59:54 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A series whose sum range is an
arbitrary finite set" by Jakub Onufry Wojtaszczyk.
Abstract: In finitely-dimensional spaces the sum range of a series
has to be an affine subspace. It is long known this is not the case in
infinitely dimensional Banach spaces. In particular in 1984 M.I. Kadets
and K. Wo\`{z}niakowski obtained an example of a series the sum range
of which consisted of two points, and asked whether it is possible to
obtain more than two, but finitely many points. This paper answers the
question positively, by showing how to obtain an arbitrary finite set
as the sum range of a series in any infinitely dimensional Banach space.
Archive classification: math.FA
Mathematics Subject Classification: 46B15
Citation: Studia Mathematica 171 (3) (2005), pp. 261-281
Remarks: 21 pages
The source file(s), npunktow.tex: 64310 bytes, is(are) stored in gzipped
form as 0803.0415.gz with size 20kb. The corresponding postcript file
has gzipped size 127kb.
Submitted from: onufryw at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0803.0415
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From alspach at fourier.math.okstate.edu Wed Mar 5 12:00:44 2008
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id 601BAD0A94; Wed, 5 Mar 2008 12:00:44 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jakub Onufry Wojtaszczyk
Message-Id: <20080305180044.601BAD0A94 at fourier.math.okstate.edu>
Date: Wed, 5 Mar 2008 12:00:44 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The square negative correlation
property for generalized Orlicz balls" by Jakub Onufry Wojtaszczyk.
Abstract: Antilla, Ball and Perissinaki proved that the squares of
coordinate functions in $\ell_p^n$ are negatively correlated. This
paper extends their results to balls in generalized Orlicz norms on
R^n. From this, the concentration of the Euclidean norm and a form of the
Central Limit Theorem for the generalized Orlicz balls is deduced. Also,
a counterexample for the square negative correlation hypothesis for
1-symmetric bodies is given.
Currently the CLT is known in full generality for convex bodies (see the
paper "Power-law estimates for the central limit theorem for convex
sets" by B. Klartag), while for generalized Orlicz balls a much more
general result is true (see "The negative association property for the
absolute values of random variables equidistributed on a generalized
Orlicz ball" by M. Pilipczuk and J. O. Wojtaszczyk). While, however,
both aforementioned papers are rather long, complicated and technical,
this paper gives a simple and elementary proof of, eg., the Euclidean
concentration for generalized Orlicz balls.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 52A20, 60D05
Citation: Geometric Aspects of Functional Analysis, Israel Seminar,
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0803.0433
or
http://arXiv.org/abs/0803.0433
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From alspach at fourier.math.okstate.edu Wed Mar 5 12:02:09 2008
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id 8C7A6D0A94; Wed, 5 Mar 2008 12:02:09 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Marcin Pilipczuk, Jakub Onufry Wojtaszczyk
Message-Id: <20080305180209.8C7A6D0A94 at fourier.math.okstate.edu>
Date: Wed, 5 Mar 2008 12:02:09 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The negative association property
for the absolute values of random variables equidistributed on a
generalized Orlicz ball" by Marcin Pilipczuk, Jakub Onufry Wojtaszczyk.
Abstract: Random variables equidistributed on convex bodies have received
quite a lot of attention in the last few years. In this paper we prove the
negative association property (which generalizes the subindependence of
coordinate slabs) for generalized Orlicz balls. This allows us to give
a strong concentration property, along with a few moment comparison
inequalities. Also, the theory of negatively associated variables is
being developed in its own right, which allows us to hope more results
will be available. Moreover, a simpler proof of a more general result
for $\ell_p^n$ balls is given.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 52A20, 60D05
Remarks: 44 pages (sorry)
The source file(s), dlaorlic.tex: 166228 bytes, is(are) stored in gzipped
form as 0803.0434.gz with size 46kb. The corresponding postcript file
has gzipped size 253kb.
Submitted from: onufryw at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0803.0434
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From alspach at fourier.math.okstate.edu Wed Mar 5 12:03:25 2008
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id E42C4D0A94; Wed, 5 Mar 2008 12:03:25 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by K. J. Swanepoel
Message-Id: <20080305180325.E42C4D0A94 at fourier.math.okstate.edu>
Date: Wed, 5 Mar 2008 12:03:25 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Vertex degrees of Steiner
minimal trees in $\ell_p^d$ and other smooth Minkowski spaces" by
K. J. Swanepoel.
Abstract: We find upper bounds for the degrees of vertices and Steiner
points in Steiner Minimal Trees in the d-dimensional Banach spaces
\ell_p^d independent of d. This is in contrast to Minimal Spanning Trees,
where the maximum degree of vertices grows exponentially in d (Robins
and Salowe, 1995). Our upper bounds follow from characterizations of
singularities of SMT's due to Lawlor and Morgan (1994), which we extend,
and certain \ell_p-inequalities. We derive a general upper bound of d+1
for the degree of vertices of an SMT in an arbitrary smooth d-dimensional
Banach space; the same upper bound for Steiner points having been found
by Lawlor and Morgan. We obtain a second upper bound for the degrees of
vertices in terms of 1-summing norms.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 05C05 (Primary); 49Q10 (Secondary)
Citation: Discrete & Computational Geometry 21 (1999) 437-447
Remarks: 12 pages
The source file(s), steiner-lp.tex: 30143 bytes, is(are) stored in gzipped
form as 0803.0443.gz with size 10kb. The corresponding postcript file
has gzipped size 81kb.
Submitted from: konrad.swanepoel at gmail.com
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http://front.math.ucdavis.edu/0803.0443
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From banach-bounces at math.okstate.edu Tue Mar 11 20:37:10 2008
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Date: Tue, 11 Mar 2008 20:36:24 -0500
From: Dale Alspach <alspach at math.okstate.edu>
Message-Id: <20080312013624.2BAF7DE58C at szlenk.math.okstate.edu>
Subject: [Banach] Workshop in Analysis and Probability
Reply-To: johnson at math.tamu.edu
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Workshop in Analysis and Probability
Department of Mathematics
Texas A&M University
Summer 2008
The Summer 2008 session of the Workshop in Analysis and Probability at Texas A&M University will be in session from July 7 until August 10. For information about the Workshop, consult the Workshop Home Page, URL
http://www.math.tamu.edu/research/workshops/linanalysis/
The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held August 8-10.
Julien Giol <giol at math.tamu.edu>, David Kerr (chair) <kerr at math.tamu.edu>, and Andrew Toms <atoms at mathstat.yorku.ca> are organizing a Concentration Week on "Operator Algebras, Dynamics, and Classification" which will take place August 4-8. For more information, go to
http://www.math.tamu.edu/~kerr/concweek08.html.
Ron Douglas <rdouglas at math.tamu.edu> is organizing a Concentration Week on "Multivariate Operator Theory" that will take place July 28 - August 1.
The Workshop is supported in part by grants from the National Science Foundation (NSF). Minorities, women, graduate students, and young researchers are especially encouraged to attend.
For logistical support, including requests for support, please contact Cara Barton <cara at math.tamu.edu> or Jaime Vykukal <jaime at math.tamu.edu>. For more information on the Workshop itself, please contact William Johnson <johnson at math.tamu.edu>, David Larson <larson at math.tamu.edu>, Gilles Pisier <pisier at math.tamu.edu>, or Joel Zinn <jzinn at math.tamu.edu>.
For information about the Concentration Week "Operator Algebras, Dynamics, and Classification" contact David Kerr <kerr at math.tamu.edu>.
For information about the Concentration Week on "Multivariate Operator Theory", contact Ron Douglas <rdouglas at math.tamu.edu>.
_______________________________________________
Banach mailing list
Banach at math.okstate.edu
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From alspach at fourier.math.okstate.edu Fri Mar 14 15:06:40 2008
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id 31F08D0595; Fri, 14 Mar 2008 15:06:40 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Manor Mendel and Assaf Naor
Message-Id: <20080314200640.31F08D0595 at fourier.math.okstate.edu>
Date: Fri, 14 Mar 2008 15:06:40 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Markov convexity and local rigidity
of distorted metrics" by Manor Mendel and Assaf Naor.
Abstract: The geometry of discrete tree metrics is studied from the
following perspectives:
1. Markov p-convexity, which was shown by Lee, Naor, and Peres to be a
property of p-convex Banach space, is shown here to be equivalent to
p-convexity of Banach spaces.
2. On the other hand, there exists an example of a metric space which
is not Markov p-convex for any finite p, but does not uniformly contain
complete binary trees. Note that the previous item implies that Banach
spaces contain complete binary trees uniformly if and only if they are
not Markov p-convex for any finite p.
3. For every B>4, a metric space X is constructed such that all
tree metrics can be embedded in X with distortion at most B, but when
large complete binary trees are embedded in X, the distortion tends to
B. Therefore the class of finite tree metrics do exhibit a dichotomy
in the distortions achievable when embedding them in other metric
spaces. This is in contrast to the dichotomy exhibited by the class of
finite subsets of L_1, and the class of all finite metric spaces.
Archive classification: math.MG math.FA
Remarks: 10 pages, extended abstract to appear in SoCG '08
%The source file(s), Charlie-tree-socg.bbl: 8435 bytes
Charlie-tree-socg.tex: 150202 bytes figs/3path-types.eps: 26109
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18207 bytes figs/mid-lemma2-c2b.pdf: 10699 bytes figs/mid-lemma2-c2c.eps:
21237 bytes figs/mid-lemma2-c2c.pdf: 12496 bytes figs/midpoints-new.eps:
17442 bytes figs/midpoints-new.pdf: 9662 bytes figs/tip-contract.eps:
13542 bytes figs/tip-contract.pdf: 6745 bytes figs/type-II-surprise.eps:
17919 bytes figs/type-II-where-w.eps: 11124 bytes sig-alt-full.cls:
56035 bytes, is(are) stored in gzipped
form as 0803.1697.tar.gz with size 302kb. The corresponding postcript
file has gzipped size 146kb.
Submitted from: mendelma at gmail.com
The paper may be downloaded from the archive by web browser from URL
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From alspach at fourier.math.okstate.edu Fri Mar 21 12:02:16 2008
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id 67D00D0540; Fri, 21 Mar 2008 12:02:16 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Ian Doust and Venta Terauds
Message-Id: <20080321170216.67D00D0540 at fourier.math.okstate.edu>
Date: Fri, 21 Mar 2008 12:02:16 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Extensions of an $AC(\sigma)$
functional calculus" by Ian Doust and Venta Terauds.
Abstract: On a reflexive Banach space $X$, if an operator $T$ admits
a functional calculus for the absolutely continuous functions on
its spectrum $\sigma(T) \subseteq \mathbb{R}$, then this functional
calculus can always be extended to include all the functions of bounded
variation. This need no longer be true on nonreflexive spaces. In
this paper, it is shown that on most classical separable nonreflexive
spaces, one can construct an example where such an extension is
impossible. Sufficient conditions are also given which ensure that an
extension of an $\AC$ functional calculus is possible for operators
acting on families of interpolation spaces such as the $L^p$ spaces.
Archive classification: math.FA
Mathematics Subject Classification: 47B40
The source file(s), extns-f-submit.tex: 36353 bytes, is(are) stored in
gzipped form as 0803.2131.gz with size 11kb. The corresponding postcript
file has gzipped size 84kb.
Submitted from: i.doust at unsw.edu.au
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http://front.math.ucdavis.edu/0803.2131
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From alspach at fourier.math.okstate.edu Wed Mar 26 11:59:43 2008
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id 34571D05C8; Wed, 26 Mar 2008 11:59:43 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Marianne Morillon
Message-Id: <20080326165943.34571D05C8 at fourier.math.okstate.edu>
Date: Wed, 26 Mar 2008 11:59:43 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Countable choice and compactness"
by Marianne Morillon.
Abstract: We work in set-theory without choice ZF. Denoting by AC(N)
the countable axiom of choice, we show in ZF+AC(N) that the closed unit
ball of a uniformly convex Banach space is compact in the convex topology
(an alternative to the weak topology in ZF). We prove that this ball is
(closely) convex-compact in the convex topology. Given a set I, a real
number p greater or equal to 1 (resp. . p = 0), and some closed subset
F of [0, 1]^I which is a bounded subset of l^p(I), we show that AC(N)
(resp. DC, the axiom of Dependent Choices) implies the compactness of F.
Archive classification: math.FA math.GN math.LO
Mathematics Subject Classification: 03E25, 46B26, 54D30
The source file(s), figure.tex: 548 bytes
final.bbl: 2612 bytes
final.tex: 55144 bytes
icone-ermit.eps: 24310 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0803.3131
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From alspach at fourier.math.okstate.edu Wed Mar 26 12:00:45 2008
Return-Path: <alspach at fourier.math.okstate.edu>
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id B7200D05C8; Wed, 26 Mar 2008 12:00:45 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jarno Talponen
Message-Id: <20080326170045.B7200D05C8 at fourier.math.okstate.edu>
Date: Wed, 26 Mar 2008 12:00:45 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Lindelof type of generalization
of separability in Banach spaces" by Jarno Talponen.
Abstract: We will introduce the countable separation property (CSP) of
Banach spaces X, which is defined as follows: For each subset \mathcal{F}
of X^{\ast}, which separates X, there exists a countable separating subset
\mathcal{F}_{0} of \mathcal{F}. All separable Banach spaces have CSP and
plenty of examples of non-separable CSP spaces are provided. Connections
of CSP with Markucevic-bases, Corson property and related geometric
issues are discussed.
Archive classification: math.FA
Mathematics Subject Classification: 46B26; 46A50
The source file(s), csp.tex: 62263 bytes, is(are) stored in gzipped
form as 0803.3541.gz with size 17kb. The corresponding postcript file
has gzipped size 108kb.
Submitted from: talponen at cc.helsinki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0803.3541
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http://arXiv.org/abs/0803.3541
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From alspach at fourier.math.okstate.edu Wed Mar 26 12:01:25 2008
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id D849FD05C8; Wed, 26 Mar 2008 12:01:25 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Michael Cwikel
Message-Id: <20080326170125.D849FD05C8 at fourier.math.okstate.edu>
Date: Wed, 26 Mar 2008 12:01:25 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Lecture notes on duality and
interpolation spaces" by Michael Cwikel.
Abstract: Known or essentially known results about duals of interpolation
spaces are presented, taking a point of view sometimes slightly different
from the usual one. Particular emphasis is placed on Alberto Calderon's
theorem describing the duals of his complex interpolation spaces
[A_0,A_1]_\theta. The pace is slow, since these notes are intended for
graduate students who have just begun to study interpolation spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B70 (primary) 46B10 (secondary)
Remarks: 24 pages
The source file(s), NotesOnDuality-arXiv.tex: 93949 bytes, is(are)
stored in gzipped form as 0803.3558.gz with size 25kb. The corresponding
postcript file has gzipped size 138kb.
Submitted from: mcwikel at math.technion.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0803.3558
or
http://arXiv.org/abs/0803.3558
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From alspach at fourier.math.okstate.edu Wed Apr 2 08:43:25 2008
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To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Yauhen Radyna, Yakov Radyno, and Anna Sidorik
Message-Id: <20080402134325.4CB80D090E at fourier.math.okstate.edu>
Date: Wed, 2 Apr 2008 08:43:25 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Characterizing Hilbert spaces
using Fourier transform over the field of p-adic numbers" by Yauhen
Radyna, Yakov Radyno, and Anna Sidorik.
Abstract: We characterize Hilbert spaces in the class of all Banach
spaces using Fourier transform of vector-valued functions over the field
$Q_p$ of $p$-adic numbers. Precisely, Banach space $X$ is isomorphic to a
Hilbert one if and only if Fourier transform $F: L_2(Q_p,X)\to L_2(Q_p,X)$
in space of functions, which are square-integrable in Bochner sense and
take value in $X$, is a bounded operator.
Archive classification: math.FA
Mathematics Subject Classification: 46C15, 43A25
Citation: Yauhen Radyna, Yakov Radyno, Anna Sidorik, Characterizing
Hilbert
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0803.3646
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http://arXiv.org/abs/0803.3646
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From alspach at fourier.math.okstate.edu Wed Apr 2 09:42:28 2008
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id ADE15D090E; Wed, 2 Apr 2008 09:42:28 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Anton R. Schep
Message-Id: <20080402144228.ADE15D090E at fourier.math.okstate.edu>
Date: Wed, 2 Apr 2008 09:42:28 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Products and factors of Banach
function spaces" by Anton R. Schep.
Abstract: Given two Banach function spaces we study the pointwise product
space E.F, especially for the case that the pointwise product of their
unit balls is again convex. We then give conditions on when the pointwise
product E . M(E, F)=F, where M(E,F) denotes the space of multiplication
operators from E into F.
Archive classification: math.FA
Mathematics Subject Classification: 46E30; 47B38
Remarks: 16 pages
The source file(s), product-bfs.bbl: 4503 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0803.4336
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http://arXiv.org/abs/0803.4336
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From alspach at fourier.math.okstate.edu Wed Apr 2 09:43:14 2008
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id 1C90ED090E; Wed, 2 Apr 2008 09:43:13 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Th. Schlumprecht and N. Sivakumar
Message-Id: <20080402144314.1C90ED090E at fourier.math.okstate.edu>
Date: Wed, 2 Apr 2008 09:43:14 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On the sampling and recovery
of bandlimited functions via scattered translates of the Gaussian"
by Th. Schlumprecht and N. Sivakumar.
Abstract: Let $\lambda$ be a positive number, and let $(x_j:j\in\mathbb
Z)\subset\mathbb R$ be a fixed Riesz-basis sequence, namely, $(x_j)$
is strictly increasing, and the set of functions $\{\mathbb R\ni
t\mapsto e^{ix_jt}:j\in\mathbb Z\}$ is a Riesz basis ({\it i.e.,\/}
unconditionalbasis) for $L_2[-\pi,\pi]$. Given a function $f\in
L_2(\mathbb R)$ whose Fourier transform is zero almost everywhere outside
the interval $[-\pi,\pi]$, there is a unique square-summable sequence
$(a_j:j\in\mathbb Z)$, depending on $\lambda$ and $f$, such that the
function$$I_\lambda(f)(x):=\sum_{j\in\mathbb Z}a_je^{-\lambda(x-x_j)^2},
\qquad x\in\mathbb R, $$ is continuous and square integrable on
$(-\infty,\infty)$, and satisfies the interpolatory conditions $I_\lambda
(f)(x_j)=f(x_j)$, $j\in\mathbb Z$. It is shown that $I_\lambda(f)$
converges to $f$ in $L_2(\mathbb R)$, and also uniformly on $\mathbb R$,
as $\lambda\to0^+$. A multidimensional version of this result is also
obtained. In addition, the fundamental functions for the univariate
interpolation process are defined, and some of their basic properties,
including their exponential decay for large argument, are established. It
is further shown that the associated interpolation operators are bounded
on $\ell_p(\mathbb Z)$ for every $p\in[1,\infty]$.
Archive classification: math.CA math.FA
Mathematics Subject Classification: 41A05 46E15
The source file(s), scsi1_5.tex: 93892 bytes, is(are) stored in gzipped
form as 0803.4344.gz with size 27kb. The corresponding postcript file
has gzipped size 165kb.
Submitted from: schlump at math.tamu.edu
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http://front.math.ucdavis.edu/0803.4344
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From alspach at fourier.math.okstate.edu Wed Apr 2 09:46:05 2008
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id CC5BAD090E; Wed, 2 Apr 2008 09:46:05 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Christian Le Merdy and Fedor Sukochev
Message-Id: <20080402144605.CC5BAD090E at fourier.math.okstate.edu>
Date: Wed, 2 Apr 2008 09:46:05 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Rademacher averages on
noncommutative symmetric spaces" by Christian Le Merdy and Fedor Sukochev.
Abstract: Let E be a separable (or the dual of a separable) symmetric
function space, let M be a semifinite von Neumann algebra and let E(M)
be the associated noncommutative function space. Let $(\varepsilon_k)_k$
be a Rademacher sequence, on some probability space $\Omega$. For
finite sequences $(x_k)_k of E(M), we consider the Rademacher averages
$\sum_k \varepsilon_k\otimes x_k$ as elements of the noncommutative
function space $E(L^\infty(\Omega)\otimes M)$ and study estimates for
their norms $\Vert \sum_k \varepsilon_k \otimes x_k\Vert_E$ calculated
in that space. We establish general Khintchine type inequalities in
this context. Then we show that if E is 2-concave, the latter norm is
equivalent to the infimum of $\Vert (\sum y_k^*y_k)^{\frac{1}{2}}\Vert +
\Vert (\sum z_k z_k^*)^{\frac{1}{2}}\Vert$ over all $y_k,z_k$ in E(M)
such that $x_k=y_k+z_k$ for any k. Dual estimates are given when E is
2-convex and has a non trivial upper Boyd index. We also study Rademacher
averages for doubly indexed families of E(M).
Archive classification: math.FA math.OA
Mathematics Subject Classification: 46L52; 46M35; 47L05
The source file(s), KHTot.tex: 72248 bytes, is(are) stored in gzipped
form as 0803.4404.gz with size 20kb. The corresponding postcript file
has gzipped size 152kb.
Submitted from: clemerdy at univ-fcomte.fr
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http://front.math.ucdavis.edu/0803.4404
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http://arXiv.org/abs/0803.4404
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From alspach at fourier.math.okstate.edu Wed Apr 2 09:47:05 2008
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id AB981D090E; Wed, 2 Apr 2008 09:47:05 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Christian Le Merdy, Eric Ricard, and Jean Roydor
Message-Id: <20080402144705.AB981D090E at fourier.math.okstate.edu>
Date: Wed, 2 Apr 2008 09:47:05 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Completely 1-complemented subspaces
of Schatten spaces" by Christian Le Merdy, Eric Ricard, and Jean Roydor.
Abstract: We consider the Schatten spaces S^p in the framework of
operator space theory and for any $1\leq p\not=2<\infty$, we characterize
the completely 1-complemented subspaces of S^p. They turn out to be
the direct sums of spaces of the form S^p(H,K), where H,K are Hilbert
spaces. This result is related to some previous work of Arazy-Friedman
giving a description of all 1-complemented subspaces of S^p in terms
of the Cartan factors of types 1-4. We use operator space structures on
these Cartan factors regarded as subspaces of appropriate noncommutative
L^p-spaces. Also we show that for any $n\geq 2$, there is a triple
isomorphism on some Cartan factor of type 4 and of dimension 2n which
is not completely isometric, and we investigate L^p-versions of such
isomorphisms.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 46L07; 46L89; 17C65
Remarks: To be pubished in the Transactions of the American Mathematical
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0803.4408
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http://arXiv.org/abs/0803.4408
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From alspach at fourier.math.okstate.edu Wed Apr 2 09:48:16 2008
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id A2C61D090E; Wed, 2 Apr 2008 09:48:16 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Marius Junge and Christian Le Merdy
Message-Id: <20080402144816.A2C61D090E at fourier.math.okstate.edu>
Date: Wed, 2 Apr 2008 09:48:16 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Dilations and rigid factorisations
on noncommutative L^p-spaces" by Marius Junge and Christian Le Merdy.
Abstract: We study some factorisation and dilation properties of
completely positive maps on noncommutative L^p-spaces. We show that
Akcoglu's dilation theorem for positive contractions on classical
(=commutative) L^p-spaces has no reasonable analog in the noncommutative
setting. Our study relies on non symmetric analogs of Pisier's operator
space valued noncommutative L^p-spaces that we investigate in the first
part of the paper.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 46L07, 46L51, 48B28
Remarks: To be published in Journal of Functional Analysis
The source file(s), JLRevised.tex: 91495 bytes, is(are) stored in gzipped
form as 0803.4410.gz with size 26kb. The corresponding postcript file
has gzipped size 178kb.
Submitted from: clemerdy at univ-fcomte.fr
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http://front.math.ucdavis.edu/0803.4410
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From alspach at fourier.math.okstate.edu Wed Apr 2 09:49:05 2008
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id E738BD090E; Wed, 2 Apr 2008 09:49:05 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Marianne Morillon
Message-Id: <20080402144905.E738BD090E at fourier.math.okstate.edu>
Date: Wed, 2 Apr 2008 09:49:05 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Uniform Eberlein spaces and the
finite axiom of choice" by Marianne Morillon.
Abstract: We work in set-theory without choice $\ZF$. Given a closed
subset $F$ of $[0,1]^I$ which is a bounded subset of $\ell^1(I)$ ({\em
resp.} such that $F \subseteq \ell^0(I)$), we show that the countable
axiom of choice for finite subsets of $I$, ({\em resp.} the countable
axiom of choice $\ACD$) implies that $F$ is compact. This enhances
previous results where $\ACD$ ({\em resp.} the axiom of Dependent
Choices $\DC$) was required. Moreover, if $I$ is linearly orderable (for
example $I=\IR$), the closed unit ball of $\ell^2(I)$ is weakly compact
(in $\ZF$).
Archive classification: math.FA math.GN math.LO
Mathematics Subject Classification: 03E25 , 54B10, 54D30, 46B26
The source file(s), icone-ermit.eps: 24310 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0804.0154
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From alspach at fourier.math.okstate.edu Mon Apr 7 16:44:47 2008
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id DFDEDD0AE1; Mon, 7 Apr 2008 16:44:47 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Z. Brzezniak, J. M. A. M. van Neerven, M. C. Veraar and L. Weis
Message-Id: <20080407214447.DFDEDD0AE1 at fourier.math.okstate.edu>
Date: Mon, 7 Apr 2008 16:44:47 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Ito's formula in UMD Banach spaces
and regularity of solutions of the Zakai equation" by Z. Brzezniak,
J. M. A. M. van Neerven, M. C. Veraar and L. Weis.
Abstract: Using the theory of stochastic integration for processes
with values in a UMD Banach space developed recently by the authors,
an Ito formula is proved which is applied to prove the existence of
strong solutions for a class of stochastic evolution equations in UMD
Banach spaces. The abstract results are applied to prove regularity in
space and time of the solutions of the Zakai equation.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 60H15; 28C20; 35R60; 46B09; 60B11
Remarks: Accepted for publication in Journal of Differential Equations
The source file(s), zakai_01_04-2008_arxiv.tex: 83664 bytes, is(are)
stored in gzipped form as 0804.0302.gz with size 25kb. The corresponding
postcript file has gzipped size 148kb.
Submitted from: mark at profsonline.nl
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http://front.math.ucdavis.edu/0804.0302
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From alspach at fourier.math.okstate.edu Mon Apr 7 16:45:52 2008
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id 13D61D0AE1; Mon, 7 Apr 2008 16:45:51 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Emanuel Milman
Message-Id: <20080407214552.13D61D0AE1 at fourier.math.okstate.edu>
Date: Mon, 7 Apr 2008 16:45:51 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On the role of convexity in
functional and isoperimetric inequalities" by Emanuel Milman.
Abstract: This is a continuation of our previous work
http://arxiv.org/abs/0712.4092. It is well known that various
isoperimetric inequalities imply their functional ``counterparts'', but in
general this is not an equivalence. We show that under certain convexity
assumptions (e.g. for log-concave probability measures in Euclidean
space), the latter implication can in fact be reversed for very general
inequalities, generalizing a reverse form of Cheeger's inequality due
to Buser and Ledoux. We develop a coherent single framework for passing
between isoperimetric inequalities, Orlicz-Sobolev functional inequalities
and capacity inequalities, the latter being notions introduced by Maz'ya
and extended by Barthe--Cattiaux--Roberto. As an application, we extend
the known results due to the latter authors about the stability of the
isoperimetric profile under tensorization, when there is no Central-Limit
obstruction. As another application, we show that under our convexity
assumptions, $q$-log-Sobolev inequalities ($q \in [1,2]$) are equivalent
to an appropriate family of isoperimetric inequalities, extending results
of Bakry--Ledoux and Bobkov--Zegarlinski. Our results extend to the more
general setting of Riemannian manifolds with density which satisfy the
$CD(0,\infty)$ curvature-dimension condition of Bakry--\'Emery.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 32F32, 26D10, 46E35, 31C15
Remarks: 42 pages
The source file(s), Dingir120.eps: 7755 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0804.0453
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http://arXiv.org/abs/0804.0453
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From alspach at fourier.math.okstate.edu Mon Apr 7 16:47:06 2008
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id A11FAD0AE1; Mon, 7 Apr 2008 16:47:06 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Miroslav Bacak and Petr Hajek
Message-Id: <20080407214706.A11FAD0AE1 at fourier.math.okstate.edu>
Date: Mon, 7 Apr 2008 16:47:06 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Mazur intersection property for
Asplund spaces" by Miroslav Bacak and Petr Hajek.
Abstract: The main result of the present note states that
it is consistent with the ZFC axioms of set theory (relying on Martin's
Maximum MM axiom), that every Asplund space of density character $\om$
has a renorming with the Mazur intersection property. Combined with the
previous result of Jim\' enez and Moreno (based upon the work of Kunen
under the continuum hypothesis)
we obtain that the MIP renormability of Asplund spaces of density
$\om$ is undecidable in ZFC.
Archive classification: math.FA
Mathematics Subject Classification: 46B03
Remarks: 6 pages
The source file(s), bacak-hajek.tex: 25023 bytes, is(are) stored in
gzipped form as 0804.0583.gz with size 9kb. The corresponding postcript
file has gzipped size 70kb.
Submitted from: bacak at karlin.mff.cuni.cz
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http://front.math.ucdavis.edu/0804.0583
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From alspach at fourier.math.okstate.edu Thu Apr 10 13:43:04 2008
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id 86D14D0ADE; Thu, 10 Apr 2008 13:43:04 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by J.M.A.M. van Neerven, M.C. Veraar, and L. Weis
Message-Id: <20080410184304.86D14D0ADE at fourier.math.okstate.edu>
Date: Thu, 10 Apr 2008 13:43:04 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Stochastic evolution equations
in UMD Banach spaces" by J.M.A.M. van Neerven, M.C. Veraar, and L. Weis.
Abstract: We discuss existence, uniqueness, and space-time H\"older
regularity for solutions of the parabolic stochastic evolution
equation \[\left\{\begin{aligned} dU(t) & = (AU(t) + F(t,U(t)))\,dt +
B(t,U(t))\,dW_H(t), \qquad t\in [0,\Tend],\\
U(0) & = u_0, \end{aligned} \right. \] where $A$ generates an analytic
$C_0$-semigroup on a UMD Banach space $E$ and $W_H$ is a cylindrical
Brownian motion with values in a Hilbert space $H$. We prove that if the
mappings $F:[0,T]\times E\to E$ and $B:[0,T]\times E\to \mathscr{L}(H,E)$
satisfy suitable Lipschitz conditions and $u_0$ is $\F_0$-measurable
and bounded, then this problem has a unique mild solution, which has
trajectories in $C^\l([0,T];\D((-A)^\theta)$ provided $\lambda\ge 0$
and $\theta\ge 0$ satisfy $\l+\theta<\frac12$. Various extensions of
this result are given and the results are applied to parabolic stochastic
partial differential equations.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 47D06; 60H15; 28C20; 46B09
Remarks: Accepted for publication in Journal of Functional Analysis
The source file(s), scp_arxiv.tex: 157532 bytes, is(are) stored in gzipped
form as 0804.0932.gz with size 44kb. The corresponding postcript file
has gzipped size 241kb.
Submitted from: mark at profsonline.nl
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http://front.math.ucdavis.edu/0804.0932
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http://arXiv.org/abs/0804.0932
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From alspach at fourier.math.okstate.edu Thu Apr 10 13:45:21 2008
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id CD4FAD0ADE; Thu, 10 Apr 2008 13:45:21 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by William Arveson
Message-Id: <20080410184521.CD4FAD0ADE at fourier.math.okstate.edu>
Date: Thu, 10 Apr 2008 13:45:21 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Maximal vectors in Hilbert space
and quantum entanglement" by William Arveson.
Abstract: Given two matrix algebras $M_1$, $M_2$, the natural inclusion
of $\mathcal L^1(M_1\otimes M_2)$ in the projective tensor product
of Banach spaces $\mathcal L^1(M_1)\hat\otimes \mathcal L^1(M_2)$ is
a contraction but not an isometry; and the projective cross norm can
be restricted to the convex set $\mathcal S$ of density matrices in
$M_1\otimes M_2$to obtain a continuous convex function $E:\mathcal S\to
[1,\infty)$. We show that $E$ {\em faithfully measures entanglement} in
the sense that a state is entangled if and only if its density matrix
$A$ satisfies $E(A)>1$. Moreover, $E(A)$ is maximized at the density
matrix $A$ associated with a pure state if and only if the range of $A$
is generated by a maximally entangled unit vector.
These concrete results follow from a general analysis of norm-closed
subsets $V$ of the unit sphere of a Hilbert space $H$. A {\em maximal vector}
(for $V$) is a unit vector $\xi\in H$ whose distance to $V$ is maximum. Maximal
vectors generalize the ``maximally entangled" unit vectors of quantum
theory.
In general, under a mild regularity hypothesis on $V$ we show that
there is a {\em norm} on $\mathcal L^1(H)$ whose restriction to the convex
set $\mathcal S$ of density operators achieves its minimum precisely on
the closed convex hull of the rank one projections associated with vectors
in $V$. It achieves its maximum on a rank one projection precisely when
its unit vector is a maximal vector. This ``entanglement-measuring norm"
is unique, and computation shows it to be the projective cross norm in
the above setting of bipartite tensor products $H=H_1\otimes H_2$.
Archive classification: math.OA math.FA
Mathematics Subject Classification: 46N50,81P68, 94B27
Remarks: 25 pages
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has gzipped size 126kb.
Submitted from: arveson at math.berkeley.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0804.1140
or
http://arXiv.org/abs/0804.1140
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From alspach at fourier.math.okstate.edu Mon Apr 14 09:46:58 2008
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To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Ariel Blanco and Niels Groenbaek
Message-Id: <20080414144658.2CDF0D0ADF at fourier.math.okstate.edu>
Date: Mon, 14 Apr 2008 09:46:58 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Amenability of algebras of
approximable operators" by Ariel Blanco and Niels Groenbaek.
Abstract: We give a necessary and sufficient condition for amenability
of the Banach algebra of approximable operators on a Banach space. We
further investigate the relationship between amenability of this algebra
and factorization of operators, strengthening known results and developing
new techniques to determine whether or not a given Banach space carries
an amenable algebra of approximable operators. Using these techniques,
we are able to show, among other things, the non-amenability of the
algebra of approximable operators on Tsirelson's space.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 47L10 (primary), 16E40
(secondary)
Remarks: 20 pages, to appear in Israel Journal of Mathematics
The source file(s), OnAmenability2.tex: 82733 bytes, is(are) stored in
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