Messages from 2013
These are the messages distributed to the Banach list during 2013.
Return-path: <alspach at math.okstate.edu>
Date: Sun, 6 Jan 2013 16:38:39 -0600
Subject: Bob Phelps
From: Dale Alspach <alspachde at gmail.com>
To: banach at math.okstate.edu
I just learned from Isaac Namioka that Bob Phelps died on January 4th.
Dale Alspach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ryan Causey
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 7 Jan 2013 08:19:52 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Estimation of the Szlenk index
of Banach spaces via Schreier spaces" by Ryan Causey.
Abstract: For each ordinal $\alpha<\omega_1$, we prove the existence
of a space with a basis and Szlenk index $\omega^{\alpha+1}$ which
is universal for the class of spaces with Szlenk index not exceeding
$\omega^\alpha$. Our proof involves developing a characterization of
which Banach spaces embed into spaces with an FDD with upper Schreier
space estimates.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B28
Submitted from: rcausey at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1212.5576
or
http://arXiv.org/abs/1212.5576
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio Aviles, Antonio J. Guirao, Jose
Rodriguez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 7 Jan 2013 08:24:30 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the Bishop-Phelps-Bollobas
property for numerical radius in C(K)-spaces" by Antonio Aviles, Antonio
J. Guirao, Jose Rodriguez.
Abstract: We study the Bishop-Phelps-Bollobas property for numerical
radius within the framework of C(K) spaces. We present several
sufficient conditions on a compact space K ensuring that C(K) has the
Bishop-Phelps-Bollobas property for numerical radius. In particular,
we show that C(K) has such property whenever K is metrizable.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 47A12, 54E45
Submitted from: avileslo at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1212.6761
or
http://arXiv.org/abs/1212.6761
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Vladimir G. Troitsky and Omid Zabeti
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 7 Jan 2013 08:27:37 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Fremlin tensor products of
concavifications of Banach lattices" by Vladimir G. Troitsky and Omid
Zabeti.
Abstract: Suppose that $E$ is a uniformly complete vector lattice and
$p_1, \ldots , p_n$ are positive reals. We prove that the diagonal of
the Fremlin projective tensor product of $E_(p_1), \ldots ,E_(p_n)$
can be identified with $E_(p)$ where $p = p_1+\ldots+p_n$ and $E_(p)$
stands for the $p$-concavification of $E$. We also provide a variant of
this result for Banach lattices. This extends the main result of [BBPTT].
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46B42. Secondary: 46M05,
46B40, 46B45
Remarks: 10 pages
Submitted from: ozabeti at yahoo.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.0749
or
http://arXiv.org/abs/1301.0749
Return-path: <alspach at math.okstate.edu>
Date: Wed, 09 Jan 2013 15:36:05 -0600
From: Dale Alspach <alspach at math.okstate.edu>
To: banach at math.okstate.edu
Subject: [Banach] Ted Odell
I just learned that Edward (Ted) Odell had a heart attack and died today.
Dale Alspach
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Subject: [Banach] Research postdoctoral position in Analysis/Convex
Geometry
at Kent State
From: Dale Alspach <alspach at math.okstate.edu>
Date: Fri, 11 Jan 2013 14:55:34 -0600
To: banach at math.okstate.edu
Kent State University's Department of Mathematical Sciences invites
applications for a postdoctoral position in Analysis/Convex Geometry.The
appointment will begin August 18, 2013 and is for two academic years
with a possible extension for a third year subject to availability of
funding.
All candidates are required to have a Ph.D. in Mathematics, or
equivalent, or to expect to have received such degree by August 2013.
The position is intended for new or recent Ph.D. students who have
strong research potential.Responsibilities will include participating in
joint research projects with the existing faculty.
Kent State University is a spacious, residential campus serving more
than 42,000 students.It is situated in a small university town within 30
miles of the major metropolitan area of Cleveland, Ohio.The Department
of Mathematical Sciences is in the College of Arts and Sciences and
offers courses and programs through the doctoral level in applied
mathematics, pure mathematics and statistics.For further information
about the department, please visit the web site http://www.math.kent.edu.
To apply for this position, candidates must first visit the Kent State
jobsite at https://jobs.kent.edu to complete an Application and an
Academic Data Form. All other documents should be submitted
electronically through mathjobs.org <http://mathjobs.org>. If electronic
submission is not feasible, submission can be mailed to:
Postdoc Search Committee
Department of Mathematical Sciences
Kent State University
Kent, OH 44242-0001.
The full application should consist of an AMS coversheet (available
through the American Mathematical Society at
http://www.ams.org/profession/employment-services/coversheet/coversheet), a
cover letter, a curriculum vitae, a publication list, a research
statement, and at least three letters of reference.
Questions regarding this position may be sent to
postdoc-search at math.kent.edu
<mailto:postdoc-search at math.kent.edu>.Screening of applicants will begin
immediately and will continue until the position is filled.
Kent State University is an Equal Opportunity, Affirmative Action Employer.
_______________________________________________
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Subject: [Banach] A Celebration of The Life of Ted Odell
From: Dale Alspach <alspach at math.okstate.edu>
Date: Mon, 14 Jan 2013 13:33:56 -0600
To: banach at math.okstate.edu
There will be "A Celebration of The Life of Ted Odell" on Saturday
January 19th at 3:30pm on campus in the Main Tower (Room number MAI 212).
Following the celebration, Ted's family have invited people to attend
a buffet reception starting at 6pm at The Green Pastures. So that the family
can get a rough idea of the number of people, if you think that you
(and your guests) will attend the reception please email Linda Porras
with the number (linda at math.utexas.edu). Thanks.
Alan Reid
Chairman
Dept. of Mathematics
UT Austin
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Subject: [Banach] Conference announcement
From: "Gonzalez Ortiz, Manuel" <manuel.gonzalez at unican.es>
Date: Tue, 22 Jan 2013 11:13:12 +0000
To: "banach at cauchy.math.okstate.edu" <banach at math.okstate.edu>
(Unknown charset: <windows-1252>)
ANNOUNCEMENT OF MEETING
Operators on Banach spaces -an homage to Pietro Aiena
C.I.E.M., Castro Urdiales (Cantabria, Spain), 10th14th June 2013
Operator theory is the research field of Professor Pietro Aiena, to whom this meeting pays
a well-deserved homage.
INVITED SPEAKERS
José Bonet (Universidad Politécnica de Valencia)
Cristina Câmara (Universidade Técnica de Lisboa)
Gustavo Corach (Instituto Argentino de Matemática)
Robin Harte (Trinity College Dublin)
Francisco L. Hernández (Universidad Complutense de Madrid)
Teresa Malheiro (Universidade do Minho)
Martin Mathieu (Queen's University Belfast)
Alfonso Montes (Universidad de Sevilla)
Vladimír Müller (Czech Academy of Sciences)
Matthias Neufang (Université Lille 1)
Florian Vasilescu (Université Lille 1)
ORGANIZATION
Jesús M. F. Castillo (Universidad de Extremadura)
Manuel González Ortiz (Universidad de Cantabria)
Mostafa Mbekhta (Université Lille 1)
Camillo Trapani (Università degli studi di Palermo)
Registration and additional information
http://www.ciem.unican.es/encuentros/banach/2013/
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
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Subject: Abstract of a paper by Hossein Dehghan
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:10:08 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A characterization of inner
product spaces related to the distance" by Hossein Dehghan.
Abstract: A new refinement of the triangle inequality is presented
in normed linear spaces. Moreover, a simple characterization of inner
product spaces is obtained by using the skew-angular distance.
Archive classification: math.FA
Remarks: To appear in Math. Notes
Submitted from: h_dehghan at iasbs.ac.ir
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.1001
or
http://arXiv.org/abs/1301.1001
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mark Rudelson
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:11:22 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lecture notes on non-asymptotic
theory of random matrices" by Mark Rudelson.
Abstract: We discuss recent developments in the study of the spectral
properties of random matrices of a large fixed size, concentrating on
the extreme singular values. Bounds for the extreme singular values
were crucial in establishing several limit laws of random matrix
theory. Besides the random matrix theory itself, these bounds have
applications in geometric functional analysis and computer science.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 60B20
Remarks: Lecture notes from the AMS short course on random matrices, 44
Submitted from: rudelson at umich.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.2382
or
http://arXiv.org/abs/1301.2382
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mathieu Meyer, Carsten Schuett, and
Elisabeth M. Werner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:17:40 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Affine invariant points" by
Mathieu Meyer, Carsten Schuett, and Elisabeth M. Werner.
Abstract: We answer in the negative a question by Gruenbaum who asked
if there exists a finite basis of affine invariant points. We give a
positive answer to another question by Gruenbaum about the "size" of
the set of all affine invariant points. Related, we show that the set
of all convex bodies K, for which the set of affine invariant points
is all of n-dimensional Euclidean space, is dense in the set of convex
bodies. Crucial to establish these results, are new affine invariant
points, not previously considered in the literature.
Archive classification: math.FA
Submitted from: elisabeth.werner at case.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.2606
or
http://arXiv.org/abs/1301.2606
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Patrick J. Rabier
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:19:02 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Differentiability of quasiconvex
functions on separable Banach spaces" by Patrick J. Rabier.
Abstract: We investigate the differentiability properties of real-valued
quasiconvex functions f defined on a separable Banach space X. Continuity
is only assumed to hold at the points of a dense subset. If so, this
subset is automatically residual. Sample results that can be quoted
without involving any new concept or nomenclature are as follows: (i)
If f is usc or strictly quasiconvex, then f is Hadamard differentiable at
the points of a dense subset of X (ii) If f is even, then f is continuous
and Gateaux differentiable at the points of a dense subset of X. In
(i) or (ii), the dense subset need not be residual but, if X is also
reflexive, it contains the complement of a Haar null set. Furthermore,
(ii) remains true without the evenness requirement if the definition of
Gateaux differentiability is generalized in an unusual, but ultimately
natural, way. The full results are much more general and substantially
stronger. In particular, they incorporate the well known theorem of
Crouzeix, to the effect that every real-valued quasiconvex function on
R^N is Frechet differentiable a.e.
Archive classification: math.OC math.FA
Submitted from: rabier at imap.pitt.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.2852
or
http://arXiv.org/abs/1301.2852
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Lingxin Bao, Lixin Cheng, Qingjin Cheng and
Duanxu Dai
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:20:24 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On universally-left-stability of
Banach spaces for $\varepsilon$-isometries" by Lingxin Bao, Lixin Cheng,
Qingjin Cheng and Duanxu Dai.
Abstract: Let $X$, $Y$ be two real Banach spaces, and $\eps\geq0$. A
map $f:X\rightarrow Y$ is said to be a standard $\eps$-isometry
if $|\|f(x)-f(y)\|-\|x-y\||\leq\eps$ for all $x,y\in X$ and with
$f(0)=0$. We say that a pair of Banach spaces $(X,Y)$ is stable if
there exists $\gamma>0$ such that for every such $\eps$ and every
standard $\eps$-isometry $f:X\rightarrow Y$ there is a bounded linear
operator $T:L(f)\equiv\overline{{\rm span}}f(X)\rightarrow X$ such
that $\|Tf(x)-x\|\leq\gamma\eps$ for all $x\in X$. $X (Y)$ is said
to be left (right)-universally stable, if $(X,Y)$ is always stable
for every $Y (X)$. In this paper, we show that if a dual Banach
space $X$ is universally-left-stable, then it is isometric to a
complemented $w^*$-closed subspace of $\ell_\infty(\Gamma)$ for some
set $\Gamma$, hence, an injective space; and that a Banach space is
universally-left-stable if and only if it is a cardinality injective
space.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 46B20, 47A58 (Primary) 26E25,
46A20, 46A24 (Secondary)
Remarks: 10 pages, submitted to Acta Mathematica Sinica, English Series
Submitted from: dduanxu at 163.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.3656
or
http://arXiv.org/abs/1301.3656
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Duanxu Dai
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:21:41 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A note on the Cheng-Dong-Zhang
Theorem and its applications" by Duanxu Dai.
Abstract: In this paper, we first give a short introduction to recent
development on the stability of Banach spaces via $\eps$-isometry and
then present an application of the Cheng-Dong-Zhang Theorem to the
continuous selections of a set valued map via $\eps-$ isometries.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 46B20, 54C60 (Primary) 26E25,
46A20, 54C65 (Secondary)
Remarks: 7 pages
Submitted from: dduanxu at 163.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.3396
or
http://arXiv.org/abs/1301.3396
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Lixin Cheng, Duanxu Dai, Yunbai Dong and Yu
Zhou
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:22:54 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On $\eps$-isometry, isometry and
linear isometry" by Lixin Cheng, Duanxu Dai, Yunbai Dong and Yu Zhou.
Abstract: Let $X$, $Y$ be two real Banach spaces, and $\eps\geq0$. A
map $f:X\rightarrow Y$ is said to be a standard $\eps$-isometry
if $|\|f(x)-f(y)\|-\|x-y\||\leq\eps$ for all $x,y\in X$ and with
$f(0)=0$. We say that a pair of Banach spaces $(X,Y)$ is stable if
there exists $\gamma>0$ such that for every such $\eps$ and every
standard $\eps$-isometry $f:X\rightarrow Y$ there is a bounded linear
operator $T:L(f)\equiv\overline{{\rm span}}f(X)\rightarrow X$ such that
$\|Tf(x)-x\|\leq\gamma\eps$ for all $x\in X$. $X (Y)$ is said to be
universally left (right)-stable, if $(X,Y)$ is always stable for every $Y
(X)$. In this paper, we show first that if such an $\eps$-isometry $f$
exists, then there is a linear isometry $U:X^{**}\rightarrow Y^{**}$. Then
we prove that universally- right-stable spaces are just Hilbert spaces;
every injective space is universally-left-stable; Finally, we verify
that a Banach space $X$ which is linear isomorphic to a subspace of
$\ell_\infty$ is universally-left-stable if and only if it is linearly
isomorphic to $\ell_\infty$; and a separable space $X$ satisfying that
$(X,Y)$ is stable for every separable $Y$ if and only if $X$ is linearly
isomorphic to $c_0$.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 46B20, 47A58 (Primary) 26E25,
46A20, 46A24 (Secondary)
Remarks: 14 pages, submitted to Israel Journal of Mathematics
Submitted from: dduanxu at 163.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.3374
or
http://arXiv.org/abs/1301.3374
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Manor Mendel and Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:24:00 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Spectral calculus and Lipschitz
extension for barycentric metric spaces" by Manor Mendel and Assaf Naor.
Abstract: The metric Markov cotype of barycentric metric spaces is
computed, yielding the first class of metric spaces that are not Banach
spaces for which this bi-Lipschitz invariant is understood. It is shown
that this leads to new nonlinear spectral calculus inequalities, as well
as a unified framework for Lipschitz extension, including new Lipschitz
extension results for $CAT(0)$ targets. An example that elucidates the
relation between metric Markov cotype and Rademacher cotype is analyzed,
showing that a classical Lipschitz extension theorem of Johnson,
Lindenstrauss and Benyamini is asymptotically sharp.
Archive classification: math.MG math.FA
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.3963
or
http://arXiv.org/abs/1301.3963
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by William B. Johnson and Gideon Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:25:08 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Subspaces of $L_p$ that embed into
$L_p(\mu)$ with $\mu$ finite" by William B. Johnson and Gideon Schechtman.
Abstract: Enflo and Rosenthal proved that $\ell_p(\aleph_1)$, $1 < p <
2$, does not (isomorphically) embed into $L_p(\mu)$ with $\mu$ a finite
measure. We prove that if $X$ is a subspace of an $L_p$ space, $1< p <
2$, and $\ell_p(\aleph_1)$ does not embed into $X$, then $X$ embeds into
$L_p(\mu)$ for some finite measure $\mu$.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46B26, 46B03
Submitted from: gideon at weizmann.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.4086
or
http://arXiv.org/abs/1301.4086
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anna Kaminska and Yves Raynaud
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:26:40 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "New formulas for decreasing
rearrangements and a class of spaces" by Anna Kaminska and Yves Raynaud.
Abstract: Using a nonlinear version of the well known Hardy-Littlewood
inequalities, we derive new formulas for decreasing rearrangements
of functions and sequences in the context of convex functions. We
use these formulas for deducing several properties of the modular
functionals defining the function and sequence spaces $M_{\varphi,w}$
and $m_{\varphi,w}$ respectively, introduced earlier in \cite{HKM}
for describing the K\"othe dual of ordinary Orlicz-Lorentz spaces in
a large variety of cases ($\varphi$ is an Orlicz function and $w$
a {\it decreasing} weight). We study these $M_{\varphi,w}$ classes
in the most general setting, where they may even not be linear, and
identify their K\"othe duals with ordinary (Banach) Orlicz-Lorentz
spaces. We introduce a new class of rearrangement invariant Banach spaces
$\mathcal{M}_{\varphi,w}$ which proves to be the K\"othe biduals of the
$M_{\varphi,w}$ classes. In the case when the class $M_{\varphi,w}$
is a separable quasi-Banach space, $\mathcal{M}_{\varphi,w}$ is its
Banach envelope.
Archive classification: math.FA
Mathematics Subject Classification: 26D07, 39B62, 42B25, 46B10, 46E30
Remarks: 25 pages
Submitted from: kaminska at memphis.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.4465
or
http://arXiv.org/abs/1301.4465
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio J. Guirao and Olena Kozhushkina
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:27:57 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Bishop-Phelps-Bollob\'as
property for numerical radius in $\ell_1(\mathbb{C})$" by Antonio
J. Guirao and Olena Kozhushkina.
Abstract: We show that the set of bounded linear operators from $X$
to $X$ admits a Bishop-Phelps-Bollob\'as type theorem for numerical
radius whenever $X$ is $\ell_1(\mathbb{C})$ or $c_0(\mathbb{C})$. As
an essential tool we provide two constructive versions of the classical
Bishop-Phelps-Bollob\'as theorem for $\ell_1(\mathbb{C})$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 47A12
Submitted from: okozhush at math.kent.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.4574
or
http://arXiv.org/abs/1301.4574
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Yousef Estaremi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:29:26 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Multiplication and composition
operators between two Orlicz spaces" by Yousef Estaremi.
Abstract: In this paper we consider composition operator $C_{\varphi}
generated by nonsingular measurable transformation $T$ and multiplication
operator $M_u$ generated by measurable function $u$ between two different
Or- licz spaces, then we investigate boundedness, compactness and
essential norm of multiplication and composition operators in term of
properties of the mapping $\varphi$, the function $u$ and the measure
space $(X, \Sigma, \mu)$.
Archive classification: math.FA
Submitted from: estaremi at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.4830
or
http://arXiv.org/abs/1301.4830
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Florence Lancien and Christian Le Merdy
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:30:37 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On functional calculus properties
of Ritt operators" by Florence Lancien and Christian Le Merdy.
Abstract: We compare various functional calculus properties of Ritt
operators. We show the existence of a Ritt operator T : X --> X on some
Banach space X with the following property: T has a bounded $\H^\infty$
functional calculus with respect to the unit disc $\D$ (that is, T
is polynomially bounded) but T does not have any bounded $\H^\infty$
functional calculus with respect to a Stolz domain of $\D$ with vertex
at 1. Also we show that for an R-Ritt operator, the unconditional Ritt
condition of Kalton-Portal is equivalent to the existence of a bounded
$\H^\infty$ functional calculus with respect to such a Stolz domain.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 47A60
Submitted from: clemerdy at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.4875
or
http://arXiv.org/abs/1301.4875
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by G. Garrigos and P. Wojtaszczyk
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:31:51 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Conditional quasi-greedy bases
in Hilbert and Banach spaces" by G. Garrigos and P. Wojtaszczyk.
Abstract: We show that, for quasi-greedy bases in Hilbert spaces,
the associated conditionality constants grow at most as $O(\log
N)^{1-\epsilon}$, for some $\epsilon>0$, answering a question by
Temlyakov. We show the optimality of this bound with an explicit
construction, based on a refinement of the method of Olevskii. This
construction leads to other examples of quasi-greedy bases with large
$k_N$ in Banach spaces, which are of independent interest.
Archive classification: math.FA math.CA
Submitted from: gustavo.garrigos at uam.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.4844
or
http://arXiv.org/abs/1301.4844
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Marek Cuth
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:33:29 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Noncommutative Valdivia compacta"
by Marek Cuth.
Abstract: We prove some generalizations of results concerning Valdivia
compact spaces (equivalently spaces with a commutative retractional
skeleton) to the spaces with a retractional skeleton (not necessarily
commutative). Namely, we show that the dual unit ball of a Banach
space is Corson provided the dual unit ball of every equivalent norm
has a retractional skeleton. Another result to be mentioned is the
following. Having a compact space K, we show that K is Corson if and
only if every continuous image of K has a retractional skeleton.
Archive classification: math.FA
Mathematics Subject Classification: 46B26, 54D30
Submitted from: cuthm5am at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.5799
or
http://arXiv.org/abs/1301.5799
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sophie Grivaux and Maria Roginskaya
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:34:45 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A general approach to Read's type
constructions of operators without non-trivial invariant closed subspaces"
by Sophie Grivaux and Maria Roginskaya.
Abstract: We present a general method for constructing operators without
non-trivial invariant closed subsets on a large class of non-reflexive
Banach spaces. In particular, our approach unifies and generalizes several
constructions due to Read of operators without non-trivial invariant
subspaces on the spaces $\ell_{1}$, $c_{0}$ or $\oplus_{\ell_{2}}J$, and
without non-trivial invariant subsets on $\ell_{1}$. We also investigate
how far our methods can be extended to the Hilbertian setting, and
construct an operator on a quasireflexive dual Banach space which has
no non-trivial $w^{*}$-closed invariant subspace.
Archive classification: math.FA
Remarks: 62 p
Submitted from: grivaux at math.univ-lille1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.6143
or
http://arXiv.org/abs/1301.6143
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sophie Grivaux and Maria Roginskaya
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:35:48 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An example of a minimal action
of the free semi-group $\F^{+}_{2}$ on the Hilbert space" by Sophie
Grivaux and Maria Roginskaya.
Abstract: The Invariant Subset Problem on the Hilbert space is to
know whether there exists a bounded linear operator $T$ on a separable
infinite-dimensional Hilbert space $H$ such that the orbit $\{T^{n}x;\
n\ge 0\}$ of every non-zero vector $x\in H$ under the action of $T$
is dense in $H$. We show that there exists a bounded linear operator
$T$ on a complex separable infinite-dimensional Hilbert space $H$
and a unitary operator $V$ on $H$, such that the following property
holds true: for every non-zero vector $x\in H$, either $x$ or $Vx$ has
a dense orbit under the action of $T$. As a consequence, we obtain in
particular that there exists a minimal action of the free semi-group with
two generators $\F^{+}_{2}$ on a complex separable infinite-dimensional
Hilbert space $H$.
Archive classification: math.FA math.DS
Remarks: 10 p
Submitted from: grivaux at math.univ-lille1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.6144
or
http://arXiv.org/abs/1301.6144
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sophie Grivaux and Maria Roginskaya
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:36:48 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On Read's type operators on
Hilbert spaces" by Sophie Grivaux and Maria Roginskaya.
Abstract: Using Read's construction of operators without non-trivial
invariant subspaces/subsets on $\ell_{1}$ or $c_{0}$, we construct
examples of operators on a Hilbert space whose set of hypercyclic vectors
is ``large'' in various senses. We give an example of an operator
such that the closure of every orbit is a closed subspace, and then,
answering a question of D. Preiss, an example of an operator such that
the set of its non-hypercyclic vectors is Gauss null. This operator
has the property that it is orbit-unicellular, i.e. the family of the
closures of its orbits is totally ordered. We also exhibit an example
of an operator on a Hilbert space which is not orbit-reflexive.
Archive classification: math.FA
Citation: Int. Math. Res. Not., 2008 Art. ID rnn083, 42 pp
Remarks: This is a preprint version of the article "On Read's type
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.6226
or
http://arXiv.org/abs/1301.6226
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Balint Farkas
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 30 Jan 2013 15:38:22 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A Bohl--Bohr--Kadets type theorem
characterizing Banach spaces not containing $c_0$" by Balint Farkas.
Abstract: We prove that a separable Banach space $E$ does not contain
a copy of the space $\co$ of null-sequences if and only if for
every doubly power-bounded operator $T$ on $E$ and for every vector
$x\in E$ the relative compactness of the sets $\{T^{n+m}x-T^nx: n\in
\NN\}$ (for some/all $m\in\NN$, $m\geq 1$) and $\{T^nx:n\in \NN\}$
are equivalent. With the help of the Jacobs--de Leeuw--Glicksberg
decomposition of strongly compact semigroups the case of (not necessarily
invertible) power-bounded operators is also handled.
Archive classification: math.FA
Mathematics Subject Classification: 47A99, 46B04, 43A60
Submitted from: farkasb at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.6250
or
http://arXiv.org/abs/1301.6250
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Vladimir Temlyakov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 12:45:12 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An inequality for the entropy
numbers and its application" by Vladimir Temlyakov.
Abstract: We prove an inequality for the entropy numbers in terms of
nonlinear Kolmogorov's widths. This inequality is in a spirit of known
inequalities of this type and it is adjusted to the form convenient
in applications for $m$-term approximations with respect to a given
system. Also, we obtain upper bounds for the $m$-term approximation by
the Weak Relaxed Greedy Algorithm with respect to a system which is not
a dictionary.
Archive classification: math.MG math.FA
Submitted from: n.i.pentacaput at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1301.7624
or
http://arXiv.org/abs/1301.7624
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by V. P. Fonf, A. J. Pallares, R. J. Smith,
and S. Troyanski
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 12:47:28 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Polyhedrality in Pieces" by
V. P. Fonf, A. J. Pallares, R. J. Smith, and S. Troyanski.
Abstract: The aim of this paper is to present two tools, Theorems 4
and 7, that make the task of finding equivalent polyhedral norms on
certain Banach spaces easier and more transparent. The hypotheses of
both tools are based on countable decompositions, either of the unit
sphere S_X or of certain subsets of the dual ball of a given Banach
space X. The sufficient conditions of Theorem 4 are shown to be necessary
in the separable case. Using Theorem 7, we can unify two known results
regarding the polyhedral renorming of certain C(K) spaces, and spaces
having an (uncountable) unconditional basis. New examples of spaces
having equivalent polyhedral norms are given in the fi?nal section.
Archive classification: math.FA
Submitted from: apall at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.0160
or
http://arXiv.org/abs/1302.0160
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Spiros A. Argyros and Pavlos Motakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 12:48:55 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Non separable reflexive spaces
admitting $\ell_1$ as a unique spreading model" by Spiros A. Argyros
and Pavlos Motakis.
Abstract: Examples of non separable reflexive Banach spaces
$\mathfrak{X}_{2^{\aleph_0}}$, admitting only $\ell_1$ as a spreading
model, are presented. The definition of the spaces is based on
$\alpha$-large, $\alpha<\omega_1$ compact families of finite subsets
of the continuum. We show the existence of such families and we study
their properties. Moreover, based on those families we construct a
reflexive space $\mathfrak{X}_{2^{\aleph_0}}^\alpha$, $\alpha<\omega_1$
with density the continuum, such that every bounded non norm convergent
sequence $\{x_k\}_k$ has a subsequence generating $\ell_1^\alpha$ as a
spreading model.
Archive classification: math.FA math.CO
Mathematics Subject Classification: 46B03, 46B06, 46B26, 03E05
Remarks: 23 pages, no figures
Submitted from: pmotakis at central.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.0715
or
http://arXiv.org/abs/1302.0715
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Vitali Milman and Liran Rotem
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 12:50:50 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "alpha-concave functions and a
functional extension of mixed volumes" by Vitali Milman and Liran Rotem.
Abstract: Mixed volumes, which are the polarization of volume with respect
to the Minkowski addition, are fundamental objects in convexity. In this
note we announce the construction of mixed integrals, which are functional
analogs of mixed volumes. We build a natural addition operation + on the
class of quasi-concave functions, such that every class of \alpha-concave
functions is closed under +. We then define the mixed integrals, which
are the polarization of the integral with respect to +.
We proceed to discuss the extension of various classic inequalities
to the functional setting. For general quasi-concave functions, this
is done by restating those results in the language of rearrangement
inequalities. Restricting ourselves to \alpha-concave functions, we
state a generalization of the Alexandrov inequalities in their more
familiar form.
Archive classification: math.FA math.MG
Citation: Electron. Res. Announc. Math. Sci. 20 (2013), 1-11
Submitted from: liranro1 at post.tau.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.0823
or
http://arXiv.org/abs/1302.0823
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Wieslaw Kubis, Anibal Molto, and Stanimir
Troyanski
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 12:52:48 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Topological properties of the
continuous function spaces on some ordered compacta" by Wieslaw Kubis,
Anibal Molto, and Stanimir Troyanski.
Abstract: Some new classes of compacta $K$ are considered for which $C(K)$
endowed with the pointwise topology has a countable cover by sets of
small local norm--diameter.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 46B26, 03G10
Remarks: 11 pages
Submitted from: kubis at math.cas.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.0829
or
http://arXiv.org/abs/1302.0829
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Benoit Kloeckner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 12:54:15 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Yet another short proof of
Bourgain's distorsion estimate" by Benoit Kloeckner.
Abstract: We use a self-improvement argument to give a very short and
elementary proof of the result of Bourgain saying that regular trees do
not admit bi-Lipschitz embeddings into uniformly convex Banach spaces.
Archive classification: math.FA math.MG
Report Number: IFPREPUB
Remarks: 2 pages.
Submitted from: benoit.kloeckner at ens-lyon.org
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.1738
or
http://arXiv.org/abs/1302.1738
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stanislaw J. Szarek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 12:55:23 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On measures of symmetry and
floating bodies" by Stanislaw J. Szarek.
Abstract: We consider the following measure of symmetry of a convex
n-dimensional body K: $\rho(K)$ is the smallest constant for which there
is a point x in K such that for partitions of K by an n-1-dimensional
hyperplane passing through x the ratio of the volumes of the two
parts is at most $\rho(K)$. It is well known that $\rho(K)=1$ iff K
is symmetric. We establish a precise upper bound on $\rho(K)$; this
recovers a 1960 result of Grunbaum. We also provide a characterization
of equality cases (relevant to recent results of Nill and Paffenholz
about toric varieties) and relate these questions to the concept of
convex floating bodies.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 52A20, 52A40, 46B20
Remarks: 5 pages; this is a slightly edited manuscript from early '00s
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.2076
or
http://arXiv.org/abs/1302.2076
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Hu Bingyang, Le Hai Khoi, and Kehe Zhu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 12:58:08 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Frames and operators in Schatten
classes" by Hu Bingyang, Le Hai Khoi, and Kehe Zhu.
Abstract: Let $T$ be a compact operator on a separable Hilbert space
$H$. We show that, for $2\le p<\infty$, $T$ belongs to the Schatten
class $S_p$ if and only if $\{\|Tf_n\|\}\in \ell^p$ for \emph{every}
frame $\{f_n\}$ in $H$; and for $0<p\le2$, $T$ belongs to $S_p$ if
and only if $\{\|Tf_n\|\}\in\ell^p$ for \emph{some} frame $\{f_n\}$
in $H$. Similar conditions are also obtained in terms of the sequence
$\{\langle Tf_n,f_n\rangle\}$ and the double-indexed sequence $\{\langle
Tf_n,f_m\rangle\}$.
Archive classification: math.FA
Mathematics Subject Classification: 47B10, 46A35, 46B15
Remarks: 27 pages
Submitted from: kzhu at math.albany.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.2490
or
http://arXiv.org/abs/1302.2490
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Miek Messerschmidt and Marcel de Jeu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 12:59:39 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Right inverses of surjections
from cones onto Banach spaces" by Miek Messerschmidt and Marcel de Jeu.
Abstract: Abstract. We show that a continuous additive positively
homogeneous map from a closed not necessarily proper cone in a
Banach space onto a Banach space is an open map precisely when it
is surjective. This generalization of the usual Open Mapping Theorem
for Banach spaces is then combined with Michael's Selection Theorem to
yield the existence of a continuous bounded positively homogeneous right
inverse of such a surjective map; an improved version of the usual Open
Mapping Theorem is then a special case. As another consequence, a stronger
version of the analogue of And\^o's Theorem for an ordered Banach space
is obtained for a Banach space that is, more generally than in And\^o's
Theorem, a sum of possibly uncountably many closed not necessarily proper
cones. Applications are given for a (pre)-ordered Banach space and for
various spaces of continuous functions taking values in such a Banach
space or, more generally, taking values in an arbitrary Banach space
that is a finite sum of closed not necessarily proper cones.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47A05, Secondary 46A30,
46B20, 46B40
Submitted from: mmesserschmidt at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.2822
or
http://arXiv.org/abs/1302.2822
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Grzegorz Plebanek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 13:00:46 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On isomorphisms of Banach spaces
of continuous functions" by Grzegorz Plebanek.
Abstract: We prove that if $K$ and $L$ are compact spaces and $C(K)$
and $C(L)$ are isomorphic as Banach spaces then $K$ has a $\pi$-base
consisting of open sets $U$ such that $\overline{U}$ is a continuous
image of some compact subspace of $L$. This gives some information on
isomorphic classes of the spaces of the form $C([0,1]^\kappa)$ and $C(K)$
where $K$ is Corson compact.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B26, 46B03, 46E15
Remarks: 15 pages
Submitted from: grzes at math.uni.wroc.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.3211
or
http://arXiv.org/abs/1302.3211
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Grzegorz Plebanek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 13:02:25 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On positive embeddings of C(K)
spaces" by Grzegorz Plebanek.
Abstract: We investigate isomorphic embeddings $T: C(K)\to C(L)$
between Banach spaces of continuous functions. We show that if such an
embedding $T$ is a positive operator then $K$ is an image of $L$ under a
upper semicontinuous set-function having finite values. Moreover we show
that $K$ has a $\pi$-base of sets which closures a continuous images of
compact subspaces of $L$. Our results imply in particular that if $C(K)$
can be positively embedded into $C(L)$ then some topological properties
of $L$, such as countable tightness of Frechetness, pass to the space $K$.
We show that some arbitrary isomorphic embeddings $C(K)\to C(L)$
can be, in a sense, reduced to positive embeddings.
Archive classification: math.FA
Submitted from: grzes at math.uni.wroc.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.4360
or
http://arXiv.org/abs/1302.4360
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Claudia Correa and Daniel V. Tausk
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 13:03:52 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Extension property and
complementation of isometric copies of continuous functions spaces"
by Claudia Correa and Daniel V. Tausk.
Abstract: In this article we prove that every isometric copy of C(L)
in C(K) is complemented if L is compact Hausdorff of finite height and
K is a compact Hausdorff space satisfying the extension property, i.e.,
every closed subset of K admits an extension operator. The space C(L)
can be replaced by its subspace C(L|F) consisting of functions that
vanish on a closed subset F of L. In particular, we obtain that every
isometric copy of c_0(I) in C(K) is complemented, if K has the extension
property. Finally, we study the class of spaces having the extension
property, establishing some closure results for this class and relating
it to other classes of compact spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46E15, 54G12
Remarks: 9 pages
Submitted from: tausk at ime.usp.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.4661
or
http://arXiv.org/abs/1302.4661
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jaegil Kim and Artem Zvavitch
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 13:05:21 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Stability of the reverse
Blaschke-Santalo inequality for unconditional convex bodies" by Jaegil
Kim and Artem Zvavitch.
Abstract: Mahler's conjecture asks whether the cube is a minimizer for
the volume product of a body and its polar in the class of symmetric
convex bodies in R^n. The corresponding inequality to the conjecture
is sometimes called the the reverse Blaschke-Santalo inequality. The
conjecture is known in dimension two and in several special cases. In
the class of unconditional convex bodies, Saint Raymond confirmed
the conjecture, and Meyer and Reisner, independently, characterized
the equality case. In this paper we present a stability version of
these results and also show that any symmetric convex body, which is
sufficiently close to an unconditional body, satisfies the the reverse
Blaschke-Santalo inequality.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 52A20, 53A15, 52B10
Submitted from: jkim at math.kent.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.5719
or
http://arXiv.org/abs/1302.5719
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikhail I. Ostrovskii
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 13:08:15 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On metric characterizations of
the Radon-Nikodym and related properties of Banach spaces" by Mikhail
I. Ostrovskii.
Abstract: We find a class of metric structures which do not admit
bilipschitz embeddings into Banach spaces with the Radon-Nikod\'ym
property. Our proof relies on Chatterji's (1968) martingale
characterization of the RNP and does not use the Cheeger's (1999) metric
differentiation theory. The class includes the infinite diamond and both
Laakso (2000) spaces. We also show that for each of these structures there
is a non-RNP Banach space which does not admit its bilipschitz embedding.
We prove that a dual Banach space does not have the RNP if and only
if it admits a bilipschitz embedding of the infinite diamond.
The paper also contains related characterizations of reflexivity and the
infinite tree property.
Archive classification: math.FA math.MG
Mathematics Subject Classification: Primary: 46B22, Secondary: 05C12,
30L05, 46B10, 46B85, 54E35
Submitted from: ostrovsm at stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.5968
or
http://arXiv.org/abs/1302.5968
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Oleg Reinov and Asfand Fahad
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 13:09:38 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On dentability in locally convex
vector spaces" by Oleg Reinov and Asfand Fahad.
Abstract: For a locally convex vector space (l.c.v.s.) $E$ and an
absolutely convex neighborhood $V$ of zero, a bounded subset $A$ of $E$
is said to be $V$-dentable (respectively, $V$-f-dentable) if for any
$\epsilon>0$ there exists an $x\in A$ so that $$x\notin \overline{co}
(A\setminus (x+\epsilon V)) $$ (respectively, so that $$ x\notin {co}
(A\setminus (x+\epsilon V)) ). $$ Here, "$\overline{co}$" denotes the
closure in $E$ of the convex hull of a set. We present a theorem which
says that for a wide class of bounded subsets $B$ of locally convex vector
spaces the following is true: $(V)$ every subset of $B$ is $V$-dentable
if and only if every subset of $B$ is $V$-f-dentable. The proof is purely
geometrical and independent of any related facts. As a consequence (in the
particular case where $B$ is complete convex bounded metrizable subset
of a l.c.v.s.), we obtain a positive solution to a 1978-hypothesis of
Elias Saab (see p. 290 in "On the Radon-Nikodym property in a class of
locally convex spaces", Pacific J. Math. 75, No. 1, 1978, 281-291).
Archive classification: math.FA
Remarks: 5 pages, AMSTeX
Submitted from: orein51 at mail.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.6019
or
http://arXiv.org/abs/1302.6019
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Matthieu Fradelizi and Arnaud Marsiglietti
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 13:11:17 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the analogue of the concavity
of entropy power in the Brunn-Minkowski theory" by Matthieu Fradelizi
and Arnaud Marsiglietti.
Abstract: Elaborating on the similarity between the entropy
power inequality and the Brunn-Minkowski inequality, Costa and Cover
conjectured in {\it On the similarity of the entropy power inequality and
the Brunn-Minkowski inequality} (IEEE Trans. Inform. Theory 30 (1984),
no. 6, 837-839) the $\frac{1}{n}$-concavity of the outer parallel volume
of measurable sets as an analogue of the concavity of entropy power. We
investigate this conjecture and study its relationship with geometric
inequalities.
Archive classification: math.FA cs.IT math.IT math.MG
Mathematics Subject Classification: 52A40, 94A17
Submitted from: matthieu.fradelizi at univ-mlv.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.6093
or
http://arXiv.org/abs/1302.6093
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kania and Tomasz Kochanek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 13:13:06 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Steinhaus' lattice-point problem
for Banach spaces" by Tomasz Kania and Tomasz Kochanek.
Abstract: Given a positive integer $n$, one may find a circle surrounding
exactly $n$ points of the integer lattice. This classical geometric
fact due to Steinhaus has been recently extended to Hilbert spaces
by Zwole\'{n}ski, who replaced the integer lattice by any infinite
set which intersects every ball in at most finitely many points. We
investigate the norms satisfying this property, which we call (S),
and show that all strictly convex norms have (S). Nonetheless, we
construct a norm in dimension three which has (S) but fails to be strictly
convex. Furthermore, the problem of finding an equivalent norm enjoying
(S) is studied. With the aid of measurable cardinals, we prove that there
exists a Banach space having (S) but with no strictly convex renorming.
Archive classification: math.FA
Submitted from: t.kania at lancaster.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.6443
or
http://arXiv.org/abs/1302.6443
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ondrej F.K. Kalenda and Jiri Spurny
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 27 Feb 2013 13:15:04 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On quantitative Schur and
Dunford-Pettis properties" by Ondrej F.K. Kalenda and Jiri Spurny.
Abstract: We show that the dual to any subspace of $c_0(\Gamma)$ has the
strongest possible quantitative version of the Schur property. Further,
we establish relationship between the quantitative Schur property and
quantitative versions of the Dunford-Pettis property. Finally, we apply
these results to show, in particular, that any subspace of the space of
compact operators on $\ell_p$ ($1<p<\infty$) with Dunford-Pettis property
satisfies automatically both its quantitative versions.
Archive classification: math.FA
Mathematics Subject Classification: 46B25
Remarks: 10 pages
Submitted from: kalenda at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.6369
or
http://arXiv.org/abs/1302.6369
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Positivity VII
Date: Thu, 28 Feb 2013 09:11:55 -0600
From: Dale Alspach <alspach at math.okstate.edu>
The seventh Positivity conference will be held from July 22-26, 2013, at
the science campus of Leiden University, The Netherlands, jointly organized
by Leiden University and Delft University of Technology.
As with earlier issues, the conference is dedicated to ordered structures
and their applications in a broad sense, including topics such as ordered
Banach spaces and their operators, ordered Banach algebras, ordering in
operator algebras, etc.
Invited speakers, all confirmed:
Francesco Altomare (Bari, Italy)
Wolfgang Arendt (Ulm, Germany)
Karim Boulabiar (Tunis, Tunisia)
Qingying Bu (University, Mississippi, USA)
Guillermo Curbera (Sevilla, Spain)
Julio Flores (Madrid, Spain)
Yehoram Gordon (Haifa, Israel)
Rien Kaashoek (Amsterdam, The Netherlands)
Coenraad Labuschagne (Johannesburg, South Africa)
Boris Mordukhovich (Detroit, Michigan, USA)
Jan van Neerven (Delft, The Netherlands)
Ioannis Polyrakis (Athens, Greece)
Abdelaziz Rhandi (Salerno, Italy)
Evgeny Semenov (Voronezh, Russia)
Fedor Sukochev (Sydney, Australia)
Jun Tomiyama (Tokyo, Japan)
All participants will be given the opportunity for a 30 minute contributed
talk.
More details, and a list of the currently 130 pre-registered participants,
can be found at
http://websites.math.leidenuniv.nl/positivity2013/
For further information, or for inclusion in the mailing list of the
conference, please contact the organizers at <positivity2013 at gmail.com>.
*********************************************************
------------------------------------------------------------------------
Marcel de Jeu
Leiden University Tel. (office) +31 (0)71 527 7118
Mathematical Institute Tel. (general) +31 (0)71 527 7111
P.O. Box 9512 Fax +31 (0)71 527 7101
2300 RA Leiden email mdejeu at math.leidenuniv.nl
The Netherlands URL http://www.math.leidenuniv.nl/~mdejeu/
------------------------------------------------------------------------
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Nassif Ghoussoub Blog: Honoring Friends
From: Dale Alspach <alspach at math.okstate.edu>
Date: Mon, 25 Mar 2013 12:56:14 -0500
To: banach at math.okstate.edu
http://nghoussoub.com/2013/03/24/bill-joram-olek-ted-and-bob/
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Piotr W. Nowak
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 26 Mar 2013 10:34:00 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Group actions on Banach spaces"
by Piotr W. Nowak.
Abstract: Recently there has been growing interest in extending Kazhdan's
property (T) to other Banach spaces, but even for such familiar classes
as the Lebesgue spaces $L_p$, or even spaces isomorphic to the Hilbert
space, this program proved to be challenging. Our goal in this survey is
to give a fairly complete account of the recent developments and their
applications. We purposely focus only on the case of Banach spaces
which are not Hilbert spaces, discussing the latter case mainly as
motivation. Wa also discuss metrically proper actions on Banach spaces,
their interplay with fixed point properties and geometric applications.
Archive classification: math.GR math.DS math.FA math.OA
Submitted from: pnowak at mimuw.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.6609
or
http://arXiv.org/abs/1302.6609
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kania, Piotr Koszmider and Niels
Jakob Laustsen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 26 Mar 2013 10:37:54 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A weak*-topological dichotomy
with applications in operator theory" by Tomasz Kania, Piotr Koszmider
and Niels Jakob Laustsen.
Abstract: Denote by $[0,\omega_1)$ the locally compact Hausdorff space
consisting of all countable ordinals, equipped with the order topology,
and let $C_0[0,\omega_1)$ be the Banach space of scalar-valued,
continuous functions which are defined on $[0,\omega_1)$ and vanish
eventually. We show that a weakly$^*$ compact subset of the dual space
of $C_0[0,\omega_1)$ is either uniformly Eberlein compact, or it contains
a homeomorphic copy of the ordinal interval $[0,\omega_1]$.
Using this result, we deduce that a Banach space which is a quotient of
$C_0[0,\omega_1)$ can either be embedded in a Hilbert-generated Banach
space, or it is isomorphic to the direct sum of $C_0[0,\omega_1)$ and
a subspace of a Hilbert-generated Banach space. Moreover, we obtain a
list of eight equivalent conditions describing the Loy--Willis ideal,
which is the unique maximal ideal of the Banach algebra of bounded,
linear operators on $C_0[0,\omega_1)$. As a consequence, we find that
this ideal has a bounded left approximate identity, thus solving a
problem left open by Loy and Willis, and we give new proofs, in some
cases of stronger versions, of several known results about the Banach
space $C_0[0,\omega_1)$ and the operators acting on it.
Archive classification: math.FA math.GN
Submitted from: t.kania at lancaster.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1303.0020
or
http://arXiv.org/abs/1303.0020
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Robert Deville and Oscar Madiedo
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 26 Mar 2013 10:39:46 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A characterization of the
Radon-Nikodym property" by Robert Deville and Oscar Madiedo.
Abstract: It is well known that every bounded below and non increasing
sequence in the real line converges. We give a version of this result
valid in Banach spaces with the Radon-Nikodym property, thus extending
a former result of A. Proch\'azka.
Archive classification: math.FA
Mathematics Subject Classification: 91A05, 46B20, 46B22
Remarks: 10 pages, 2 figures
Submitted from: oscar.reynaldo at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1303.1721
or
http://arXiv.org/abs/1303.1721
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A. Manoussakis and A. Pelczar-Barwacz
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 26 Mar 2013 10:45:09 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Types of tightness in spaces with
unconditional basis" by A. Manoussakis and A. Pelczar-Barwacz.
Abstract: We present a reflexive Banach space with an unconditional
basis which is quasi-minimal and tight by range, i.e. of type (4) in
Ferenczi-Rosendal list within the framework of Gowers' classification
program of Banach spaces, but contrary to the recently constructed space
of type (4) also tight with constants, thus essentially extending the
list of known examples in Gowers classification program. The space is
defined on the base on a boundedly modified mixed Tsirelson space with
use of a special coding function.
Archive classification: math.FA
Mathematics Subject Classification: 46B03
Submitted from: amanousakis at isc.tuc.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1303.2370
or
http://arXiv.org/abs/1303.2370
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gideon Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 26 Mar 2013 10:51:13 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Matrix subspaces of $L_1$" by
Gideon Schechtman.
Abstract: If $E=\{e_i\}$ and $F=\{f_i\}$ are two 1-unconditional basic
sequences in $L_1$ with $E$ $r$-concave and $F$ $p$-convex, for some
$1\le r<p\le 2$, then the space of matrices $\{a_{i,j}\}$ with norm
$\|\{a_{i,j}\}\|_{E(F)}=\big\|\sum_k \|\sum_l a_{k,l}f_l\|e_k\big\|$
embeds into $L_1$. This generalizes a recent result of Prochno and
Sch\"utt.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46B45, 46B15
Submitted from: gideon at weizmann.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1303.4590
or
http://arXiv.org/abs/1303.4590
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Workshop at A&M
From: Bill Johnson <johnson at math.tamu.edu>
Date: Thu, 11 Apr 2013 15:14:16 -0500 (CDT)
To: banach at math.okstate.edu
Workshop in Analysis and Probability
Department of Mathematics
Texas A&M University
Summer 2013
The Summer 2013 Workshop in Analysis and Probability at Texas A&M
University will be in session from July 15 until August 16, 2013. For
information about the Workshop, consult the Workshop Home Page, whose URL
is
http://www.math.tamu.edu/~kerr/workshop/
The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held
August 2-4. SUMIRFAS will be dedicated to the memory of Ted Odell, who was
one of the organizers of the UTAMIRFAS, the predecessor of SUMIRFAS. Ted
served on the advisory board of the Workshop since its beginning.
Plenary speakers at SUMIRFAS include Stephen Dilworth, Steve Jackson,
Masoud Khalkhali, Thomas Schlumprecht, Nicole Tomczak-Jaegermann, and
Wilhelm Winter.
August 5-9 there will be a Concentration Week on "Dynamics, Geometry, and
Operator Algebras", organized by David Kerr and Guoliang Yu. This
Concentration Week aims to promote connections between nuclearity, nuclear
dimension, group C*-algebras and crossed products, topological and
measurable dynamics, algebraic dynamics, entropy, dimensional ideas from
coarse geometry, and K-theory with applications to topology. The program
will feature lecture series by David Kerr, Stuart White, and Rufus
Willett. The URL for this Concentration Week is
http://www.math.tamu.edu/~kerr/concweek13/
Immediately preceding SUMIRFAS, on August 1, there will be a celebration
of "The Mathematical Legacy of Ted Odell", organized by Thomas
Schlumprecht.
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>. For more information on the Workshop
itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr
<kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>.
For information about the Concentration Week on "Dynamics, Geometry, and
Operator Algebras" contact David Kerr <kerr at math.tamu.edu>.
For information about the day devoted to "The Mathematical Legacy of Ted
Odell" contact Thomas Schlumprecht <schlump at math.tamu.edu>
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Beltita, Sasmita Patnaik, and Gary
Weiss
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Apr 2013 13:46:15 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "$B(H)$-Commutators: A historical
survey II and recent advances on commutators of compact operators"
by Daniel Beltita, Sasmita Patnaik, and Gary Weiss.
Abstract: A sequel to \cite{gW05}, we address again the single commutator
problem \cite{PT71} of Pearcy and Topping: Is every compact operator
a single commutator of compact operators? by focusing on a 35 year
old test question for this posed in 1976 by the last named author
and others: Are there any strictly positive operators that are single
commutators of compact operators? The latter we settle here affirmatively
with a modest modification of Anderson's fundamental construction
\cite{jA77} constructing compact operators whose commutator is a rank
one projection. Moreover we provide here a rich class of such strictly
positive operators that are commutators of compact operators and pose
a question for the rest.
We explain also how these methods are related to the study of staircase
matrix forms, their equivalent block tri-diagonal forms, and commutator
problems. In particular, we present the original test question and
solution that led to the negative solution of the Pearcy-Topping question
on whether or not every trace class trace zero operator was a commutator
(or linear combination of commutators) of Hilbert-Schmidt operators. And
we show how this evolved from staircase form considerations along with
a Larry Brown result on trace connections to ideals \cite{lB94} which
itself is at the core of \cite[Section 7]{DFWW}.
The omission in \cite{gW05} of this important 35 year old test question
was inadvertent and we correct that in this paper. This sequel starts
where [ibid] left off but can be read independently of [ibid].
The present paper also has a section on self-commutator equations
$[X^*,X]=A$ within the framework of some classical operator Lie
algebras. That problem was solved by Fan and Fong (1980) for the full
algebra of compact operators, and we solve it here for the complex
symplectic Lie algebra of compact operators and for complex semisimple
Lie algebras.
Archive classification: math.OA math.FA math.RT
Mathematics Subject Classification: Primary: 47B47, 47B10, 47L20,
Secondary: 47-02, 47L30, 17B65,
Remarks: 20 pages
Submitted from: Daniel.Beltita at imar.ro
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1303.4844
or
http://arXiv.org/abs/1303.4844
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by P. Wojtaszczyk
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Apr 2013 13:47:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On left democracy function"
by P. Wojtaszczyk.
Abstract: We continue the study undertaken in \cite{GHN} of left
democracy function $h_l(N)=\inf_{\#\Lambda=N}\left\|\sum_{n\in \Lambda_N}
x_n\right\| $ of an unconditional basis in a Banach space $X$. We provide
an example of a basis with $h_l$ non-doubling. Then we show that for bases
with non-doubling $h_l$ the greedy projection is not optimal. Together
with results from \cite{GHN} and improved by C. Cabrelli, G. Garrig\'os,
E. Hernandez and U. Molter we get that the basis is greedy if and only
if the greedy projection is optimal.
Archive classification: math.FA
Submitted from: wojtaszczyk at mimuw.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1303.4972
or
http://arXiv.org/abs/1303.4972
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by David Alonso-Gutierrez and Joscha Prochno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Apr 2013 13:49:30 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Mean width of random perturbations
of random polytopes" by David Alonso-Gutierrez and Joscha Prochno.
Abstract: We prove some "high probability" results on the expected value
of the mean width for random perturbations of random polytopes. The random
perturbations are considered for Gaussian and $p$-stable random vectors,
as well as uniform distributions on $\ell_p^N$-balls and the unit sphere.
Archive classification: math.FA math.PR
Mathematics Subject Classification: Primary 52A22, Secondary 52A23, 05D40
Submitted from: joscha.prochno at jku.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1303.5677
or
http://arXiv.org/abs/1303.5677
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gero Fendler and Michael Leinert
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Apr 2013 13:50:59 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Separable $C^{\ast}$-algebras and
weak$^{\ast}$-fixed point property" by Gero Fendler and Michael Leinert.
Abstract: It is shown that the dual $\widehat{A}$ of a separable
$C^{\ast}$-algebra $A$ is discrete if and only if its Banach space dual
has the weak$^{\ast}$-fixed point property. We prove further that these
properties are equivalent to the uniform weak$^{\ast}$ Kadec-Klee property
of $A^{\ast}$ and to the coincidence of the weak$^{\ast}$ topology with
the norm topology on the pure states of $A$.
Archive classification: math.OA
Mathematics Subject Classification: Primary: 46L05, 47L50, Secondary:
46L30, 47H10
Remarks: 6 pages
Submitted from: gero.fendler at univie.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1303.5557
or
http://arXiv.org/abs/1303.5557
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. Patnaik and G. Weiss
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Apr 2013 13:53:26 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A survey on subideals of operators
and an introduction to subideal-traces" by S. Patnaik and G. Weiss.
Abstract: Operator ideals in B(H) are well understood and exploited but
ideals inside them have only recently been studied starting with the
1983 seminal work of Fong and Radjavi and continuing with two recent
articles by the authors of this survey. This article surveys this study
embodied in these three articles. A subideal is a two-sided ideal of J
(for specificity also called a J-ideal) for J an arbitrary ideal of
B(H). In this terminology we alternatively call J a B(H)-ideal.
This surveys these three articles in which we developed a complete
characterization of all J-ideals generated by sets of cardinality strictly
less than the cardinality of the continuum. So a central theme is the
impact of generating sets for subideals on their algebraic structure. This
characterization includes in particular finitely and countably generated
J-ideals. It was obtained by first generalizing to arbitrary principal
J-ideals the 1983 work of Fong-Radjavi who determined which principal
K(H)-ideals are also B(H)-ideals. A key property in our investigation
turned out to be J-softness of a B(H)-ideal I inside J, that is, IJ =
I, a generalization of a recent notion of K(H)-softness of B(H)-ideals
introduced by Kaftal-Weiss and earlier exploited for Banach spaces by
Mityagin and Pietsch. This study of subideals and the study of elementary
operators with coefficient constraints are closely related. Here we also
introduce and study a notion of subideal-traces where classical traces
(unitarily invariant linear functionals) need not make sense for subideals
that are not B(H)-ideals.
Archive classification: math.OA math.FA
Mathematics Subject Classification: Primary: 47L20, 47B10, 47B07,
Secondary: 47B47, 47B37, 13C05,
Remarks: 9 pages preprint
Submitted from: patnaisa at mail.uc.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1303.5697
or
http://arXiv.org/abs/1303.5697
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Bernhard G. Bodmann
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Apr 2013 13:54:53 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Random fusion frames are nearly
equiangular and tight" by Bernhard G. Bodmann.
Abstract: This paper demonstrates that random, independently chosen
equi-dimensional subspaces with a unitarily invariant distribution in
a real Hilbert space provide nearly tight, nearly equiangular fusion
frames. The angle between a pair of subspaces is measured in terms
of the Hilbert-Schmidt inner product of the corresponding orthogonal
projections. If the subspaces are selected at random, then a measure
concentration argument shows that these inner products concentrate near
an average value. Overwhelming success probability for near tightness
and equiangularity is guaranteed if the dimension of the subspaces is
sufficiently small compared to that of the Hilbert space and if the
dimension of the Hilbert space is small compared to the sum of all
subspace dimensions.
Archive classification: math.FA
Remarks: 12 pages AMS LaTeX, no figures
Submitted from: bgb at math.uh.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1303.5816
or
http://arXiv.org/abs/1303.5816
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Yun Sung Choi, Sun Kwang Kim, Han Ju Lee
and Miguel Martin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Apr 2013 13:56:37 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Bishop-Phelps-Bollob\'{a}s
theorem for operators on $L_1(\mu)$" by Yun Sung Choi, Sun Kwang Kim,
Han Ju Lee and Miguel Martin.
Abstract: In this paper we show that the Bishop-Phelps-Bollob\'as theorem
holds for $\mathcal{L}(L_1(\mu), L_1(\nu))$ for all measures $\mu$ and
$\nu$ and also holds for $\mathcal{L}(L_1(\mu),L_\infty(\nu))$ for every
arbitrary measure $\mu$ and every localizable measure $\nu$. Finally,
we show that the Bishop-Phelps-Bollob\'as theorem holds for two classes
of bounded linear operators from a real $L_1(\mu)$ into a real $C(K)$
if $\mu$ is a finite measure and $K$ is a compact Hausdorff space. In
particular, one of the classes includes all Bochner representable
operators and all weakly compact operators.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22
Submitted from: hanjulee at dongguk.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1303.6078
or
http://arXiv.org/abs/1303.6078
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mario Chica, Vladimir Kadets, Miguel
Martin, Soledad Moreno and Fernando Rambla
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Apr 2013 13:58:27 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Bishop-Phelps-Bollob\'as
moduli of a Banach space" by Mario Chica, Vladimir Kadets, Miguel Martin,
Soledad Moreno and Fernando Rambla.
Abstract: We introduce two Bishop-Phelps-Bollob\'as moduli of a Banach
space which measure, for a given Banach space, what is the best possible
Bishop-Phelps-Bollob\'as theorem in this space. We show that there is a
common upper bound for these moduli for all Banach spaces and we present
an example showing that this bound is sharp. We prove the continuity of
these moduli and an inequality with respect to duality. We calculate the
two moduli for Hilbert spaces and also present many examples for which
the moduli have the maximum possible value (among them, there are $C(K)$
spaces and $L_1(\mu)$ spaces). Finally, we show that if a Banach space
has the maximum possible value of any of the moduli, then it contains
almost isometric copies of the real space $\ell_\infty^{(2)}$ and present
an example showing that this condition is not sufficient.
Archive classification: math.FA
Mathematics Subject Classification: 46B04
Remarks: 26 pages, 5 figures
Submitted from: mmartins at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1304.0376
or
http://arXiv.org/abs/1304.0376
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Marek Cuth and Marian Fabian
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Apr 2013 13:59:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Projections in duals to Asplund
spaces made without Simons' lemma" by Marek Cuth and Marian Fabian.
Abstract: G. Godefroy and the second author of this note proved in
1988 that in duals to Asplund spaces there always exists a projectional
resolution of the identity. A few years later, Ch. Stegall succeeded to
drop from the original proof a deep lemma of S. Simons. Here, we rewrite
the condensed argument of Ch. Stegall in a more transparent and detailed
way. We actually show that this technology of Ch. Stegall leads to a
bit stronger/richer object ---the so called projectional skeleton---
recently constructed by W. Kubi\'s, via S. Simons' lemma and with help
of elementary submodels from logic.
Archive classification: math.FA
Submitted from: cuthm5am at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1304.1313
or
http://arXiv.org/abs/1304.1313
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Yanqi Qiu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Apr 2013 14:01:07 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A remark on the complex
interpolation for families of Banach spaces" by Yanqi Qiu.
Abstract: We show by explicit examples that the complex interpolation
for families of Banach spaces is not stable under rearrangement of the
given family on the boundary, although, by well-known results, it is
stable when the latter family takes only 2 values. In our examples,
we can even assume that the family takes only 3 values, which is best
possible. We also characterize all the transformations on the circle
that are invariant for complex interpolation at 0, they are precisely
the origin-preserving inner functions.
Archive classification: math.FA
Remarks: 19 pages
Submitted from: yqi.qiu at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1304.1403
or
http://arXiv.org/abs/1304.1403
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by H. Garth Dales, Matthew Daws, Hung Le Pham,
and Paul Ramsden
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Apr 2013 14:02:22 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Equivalence of multi-norms"
by H. Garth Dales, Matthew Daws, Hung Le Pham, and Paul Ramsden.
Abstract: The theory of multi-norms was developed by H.\ G.\ Dales and
M.\ E.\ Polyakov in a memoir that was published in \emph{Dissertationes
Mathematicae}. In that memoir, the notion of `equivalence' of multi-norms
was defined. In the present memoir, we make a systematic study of when
various pairs of multi-norms are mutually equivalent.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B28, Secondary 46M05, 47L05
Submitted from: hung.pham at vuw.ac.nz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1304.2096
or
http://arXiv.org/abs/1304.2096
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jan-David Hardtke
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Apr 2013 14:03:49 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "K\"othe-Bochner spaces and some
geometric properties related to rotundity and smoothness" by Jan-David
Hardtke.
Abstract: In 2000 Kadets et al. introduced the notions of acs, luacs and
uacs spaces, which form common generalisations of well-known rotundity
and smoothness properties of Banach spaces. In a recent preprint the
author introduced some further related notions and investigated the
behaviour of these geometric properties under the formation of absolute
sums. This paper is in a sense a continuation of the previous work. Here
we will study the behaviour of said properties under the formation of
K\"othe-Bochner spaces, thereby generalising some results of Sirotkin
on the acs, luacs and uacs properties of $L^p$-Bochner spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B20 46B42 46E30
Remarks: 40 pages, 4 figures, partial text overlap with arXiv:1201.2300
Submitted from: hardtke at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1304.2950
or
http://arXiv.org/abs/1304.2950
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Kevin Beanland and Daniel Freeman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 7 May 2013 09:53:57 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Uniformly factoring weakly compact
operators" by Kevin Beanland and Daniel Freeman.
Abstract: Let $X$ and $Y$ be separable Banach spaces. Suppose $Y$ either
has a shrinking basis or $Y$ is isomorphic to $C(2^\nn)$ and $\aaa$ is
a subset of weakly compact operators from $X$ to $Y$ which is analytic
in the strong operator topology. We prove that there is a reflexive
space with a basis $Z$ such that every $T \in \aaa$ factors through
$Z$. Likewise, we prove that if $\aaa \subset \llll(X, C(2^\nn))$ is
a set of operators whose adjoints have separable range and is analytic
in the strong operator topology then there is a Banach space $Z$ with
separable dual such that every $T \in \aaa$ factors through $Z$. Finally
we prove a uniformly version of this result in which we allow the domain
and range spaces to vary.
Archive classification: math.FA
Remarks: 19 pages, comments welcome
Submitted from: kbeanland at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1304.3471
or
http://arXiv.org/abs/1304.3471
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Julio Becerra Guerrero, Gines Lopez Perez and
Abraham Rueda Zoido
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 7 May 2013 09:55:58 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Big slices versus big relatively
weakly open subsets in Banach spaces" by Julio Becerra Guerrero, Gines
Lopez Perez and Abraham Rueda Zoido.
Abstract: We study the unknown differences between the size of slices
and relatively weakly open subsets of the unit ball in Banach spaces. We
show that every Banach space containing isomorphic copies of $c_0$ can be
equivalently renormed so that every slice of its unit ball has diameter 2
and satisfying that its unit ball contains nonempty relatively weakly open
subsets with diameter strictly less than 2, which answers by the negative
an open problem. As a consequence a Banach space is constructed satisfying
that every slice of its unit ball has diameter 2 and containing nonempty
relatively weakly open subsets of its unit ball with diameter arbitrarily
small, which stresses the differences between the size of slices and
relatively weakly open subsets of the unit ball of Banach spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B22
Remarks: 12 pages
Submitted from: glopezp at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1304.4397
or
http://arXiv.org/abs/1304.4397
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kania and Niels Jakob Laustsen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 7 May 2013 09:57:21 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Operators on two Banach spaces
of continuous functions on locally compact spaces of ordinals" by
Tomasz Kania and Niels Jakob Laustsen.
Abstract: Denote by $[0,\omega_1)$ the set of countable ordinals,
equipped with the order topology, let $L_0$ be the disjoint union of
the compact ordinal intervals $[0,\alpha]$ for $\alpha$ countable, and
consider the Banach spaces $C_0[0,\omega_1)$ and $C_0(L_0)$ consisting of
all scalar-valued, continuous functions which are defined on the locally
compact Hausdorff spaces $[0,\omega_1)$ and~$L_0$, respectively, and which
vanish eventually. Our main result states that a bounded operator $T$
between any pair of these two Banach spaces fixes a copy of $C_0(L_0)$
if and only if the identity operator on $C_0(L_0)$ factors through $T$,
if and only if the Szlenk index of $T$ is uncountable. This implies that
the set $\mathscr{S}_{C_0(L_0)}(C_0(L_0))$ of $C_0(L_0)$-strictly singular
operators on $C_0(L_0)$ is the unique maximal ideal of the Banach algebra
$\mathscr{B}(C_0(L_0))$ of all bounded operators on $C_0(L_0)$, and that
$\mathscr{S}_{C_0(L_0)}(C_0[0,\omega_1))$ is the second-largest proper
ideal of $\mathscr{B}(C_0[0,\omega_1))$. Moreover, it follows that the
Banach space $C_0(L_0)$ is primary and complementably homogeneous.
Archive classification: math.FA
Submitted from: t.kania at lancaster.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1304.4951
or
http://arXiv.org/abs/1304.4951
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Carando, Andreas Defant and Pablo
Sevilla-Peris
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 7 May 2013 09:58:48 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Bohr's absolute convergence
problem for $\mathcal{H}_p$-Dirichlet in Banach spaces" by Daniel Carando,
Andreas Defant and Pablo Sevilla-Peris.
Abstract: The Bohr-Bohnenblust-Hille Theorem states that the width of
the strip in the complex plane on which an ordinary Dirichlet series
$\sum_n a_n n^{-s}$ converges uniformly but not absolutely is less than or
equal to $1/2$, and this estimate is optimal. Equivalently, the supremum
of the absolute convergence abscissas of all Dirichlet series in the
Hardy space $\mathcal{H}_\infty$ equals $1/2$. By a surprising fact of
Bayart the same result holds true if $\mathcal{H}_\infty$ is replaced
by any Hardy space $\mathcal{H}_p$, $1 \le p < \infty$, of Dirichlet
series. For Dirichlet series with coefficients in a Banach space $X$ the
maximal width of Bohr's strips depend on the geometry of $X$; Defant,
Garc\'ia, Maestre and P\'erez-Garc\'ia proved that such maximal width
equal $1- 1/\ct(X)$, where $\ct(X)$ denotes the maximal cotype of $X$.
Equivalently, the supremum over the absolute convergence abscissas of all
Dirichlet series in the vector-valued Hardy space $\mathcal{H}_\infty(X)$
equals $1- 1/\ct(X)$. In this article we show that this result remains
true if $\mathcal{H}_\infty(X)$ is replaced by the larger class
$\mathcal{H}_p(X)$, $1 \le p < \infty$.
Archive classification: math.FA
Mathematics Subject Classification: 30B50, 32A05, 46G20
Submitted from: dcarando at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1304.5377
or
http://arXiv.org/abs/1304.5377
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by K.K. Kampoukos and S.K. Mercourakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 7 May 2013 10:00:00 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On a certain class of $\K$ Banach
spaces" by K.K. Kampoukos and S.K. Mercourakis.
Abstract: Using a strengthening of the concept of $\K$ set, introduced
in this paper, we study a certain subclass of the class of $\K$
Banach spaces; the so called strongly $\K$ Banach spaces. This class of
spaces includes subspaces of strongly weakly compactly generated (SWCG)
as well as Polish Banach spaces and it is related to strongly weakly
$\mathcal{K}$--analytic (SWKA) Banach spaces as the known classes of $\K$
and weakly $\mathcal{K}$--analytic (WKA) Banach spaces are related.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, 54H05, 03E15,
Secondary 46B26
Remarks: Topology and its Applications (to appear, 28 pages)
Submitted from: smercour at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1304.6577
or
http://arXiv.org/abs/1304.6577
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by David Preiss and Gareth Speight
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 7 May 2013 10:01:40 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Differentiability of Lipschitz
functions in Lebesgue null sets" by David Preiss and Gareth Speight.
Abstract: We show that if n>1 then there exists a Lebesgue null set in
R^n containing a point of differentiability of each Lipschitz function
mapping from R^n to R^(n-1); in combination with the work of others,
this completes the investigation of when the classical Rademacher theorem
admits a converse. Avoidance of sigma-porous sets, arising as irregular
points of Lipschitz functions, plays a key role in the proof.
Archive classification: math.FA math.CA
Mathematics Subject Classification: 46G05, 46T20
Remarks: 33 pages
Submitted from: G.Speight at Warwick.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1304.6916
or
http://arXiv.org/abs/1304.6916
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Konrad J. Swanepoel
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 7 May 2013 10:03:54 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Equilateral sets and a Sch\"utte
Theorem for the 4-norm" by Konrad J. Swanepoel.
Abstract: A well-known theorem of Sch\"utte (1963) gives a sharp lower
bound for the ratio between the maximum distance and minimum distance
between n+2 points in n-dimensional Euclidean space. In this brief
note we adapt B\'ar\'any's elegant proof of this theorem to the space
$\ell_4^n$. This gives a new proof that the largest cardinality of an
equilateral set in $\ell_4^n$ is n+1, and gives a constructive bound for
an interval $(4-\epsilon_n,4+\epsilon_n)$ of values of p close to 4 for
which it is guaranteed that the largest cardinality of an equilateral
set in $\ell_p^n$ is n+1.
Archive classification: math.MG math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 52A21, 52C17
Remarks: 5 pages
Submitted from: konrad.swanepoel at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1304.7033
or
http://arXiv.org/abs/1304.7033
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Trond Abrahamsen, Vegard Lima, and Olav
Nygaard
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 7 May 2013 10:05:24 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Remarks on diameter 2 properties"
by Trond Abrahamsen, Vegard Lima, and Olav Nygaard.
Abstract: If $X$ is an infinite-dimensional uniform algebra, if $X$
has the Daugavet property or if $X$ is a proper $M$-embedded space,
every relatively weakly open subset of the unit ball of the Banach
space $X$ is known to have diameter 2, i.e., $X$ has the diameter 2
property. We prove that in these three cases even every finite convex
combination of relatively weakly open subsets of the unit ball have
diameter 2. Further, we identify new examples of spaces with the diameter
2 property outside the formerly known cases; in particular we observe
that forming $\ell_p$-sums of diameter 2 spaces does not ruin diameter
2 structure.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B22
Remarks: To appear in Journal of Convex Analysis
Submitted from: veli at hials.no
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1304.7068
or
http://arXiv.org/abs/1304.7068
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Krzysztof Bolibok, Andrzej Wisnicki and Jacek
Wosko
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 7 May 2013 10:07:10 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The minimal displacement and
extremal spaces" by Krzysztof Bolibok, Andrzej Wisnicki and Jacek Wosko.
Abstract: We show that both separable preduals of $L_{1}$ and non-type
I $C^*$-algebras are strictly extremal with respect to the minimal
displacement of $k$-Lipschitz mappings acting on the unit ball of a Banach
space. In particular, every separable $C(K)$ space is strictly extremal.
Archive classification: math.FA
Submitted from: awisnic at hektor.umcs.lublin.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.0246
or
http://arXiv.org/abs/1305.0246
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by L.K.Vashisht and Geetika Khattar
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 7 May 2013 10:12:04 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On $\mathfrak{I}$-reconstruction
property" by L.K.Vashisht and Geetika Khattar.
Abstract: Reconstruction property in Banach spaces introduced
and studied by Casazza and Christensen in [1]. In this paper we
introduce reconstruction property in Banach spaces which satisfy
$\mathfrak{I}$-property. A characterization of reconstruction property in
Banach spaces which satisfy $\mathfrak{I}$-property in terms of frames in
Banach spaces is obtained. Banach frames associated with reconstruction
property are discussed.
Archive classification: math.FA
Mathematics Subject Classification: 42C15, 42C30, 46B15
Submitted from: lalitkvashisht at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.0334
or
http://arXiv.org/abs/1305.0334
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Marius Junge and Carlos Palazuelos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 7 May 2013 10:17:07 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Channel capacities via $p$-summing
norms" by Marius Junge and Carlos Palazuelos.
Abstract: In this paper we show how \emph{the metric theory of tensor
products} developed by Grothendieck perfectly fits in the study of
channel capacities, a central topic in \emph{Shannon's information
theory}. Furthermore, in the last years Shannon's theory has been
generalized to the quantum setting to let the \emph{quantum information
theory} step in. In this paper we consider the classical capacity of
quantum channels with restricted assisted entanglement. In particular
these capacities include the classical capacity and the unlimited
entanglement-assisted classical capacity of a quantum channel. To
deal with the quantum case we will use the noncommutative version of
$p$-summing maps. More precisely, we prove that the (product state)
classical capacity of a quantum channel with restricted assisted
entanglement can be expressed as the derivative of a completely
$p$-summing norm.
Archive classification: math.FA math.OA quant-ph
Submitted from: carlospalazuelos at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.1020
or
http://arXiv.org/abs/1305.1020
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Marek Cuth
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:12:35 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Simultaneous projectional
skeletons" by Marek Cuth.
Abstract: We prove the existence of a simultaneous projectional skeleton
for certain subspaces of $\mathcal{C}(K)$ spaces. This generalizes a
result on simultaneous projectional resolutions of identity proved by
M. Valdivia. We collect some consequences of this result. In particular
we give a new characterization of Asplund spaces using the notion of
projectional skeleton.
Archive classification: math.FA
Mathematics Subject Classification: 46B26, 54D30
Submitted from: cuthm5am at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.1438
or
http://arXiv.org/abs/1305.1438
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by David Alonso-Gutierrez, Soeren Christensen,
Markus Passenbrunner, and Joscha Prochno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:16:58 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the Distribution of Random
variables corresponding to norms" by David Alonso-Gutierrez, Soeren
Christensen, Markus Passenbrunner, and Joscha Prochno.
Abstract: Given a normalized Orlicz function $M$ we provide an easy
formula for a distribution such that, if $X$ is a random variable
distributed accordingly and $X_1,...,X_n$ are independent copies of $X$,
then the expected value of the p-norm of the vector $(x_iX_i)_{i=1}^n$
is of the order $\| x \|_M$ (up to constants dependent on p only). In case
$p=2$ we need the function $t\mapsto tM'(t) - M(t)$ to be $2$-concave and
as an application immediately obtain an embedding of the corresponding
Orlicz spaces into $L_1[0,1]$. We also provide a general result replacing
the $\ell_p$-norm by an arbitrary $N$-norm. This complements some deep
results obtained by Gordon, Litvak, Sch\"utt, and Werner. We also
prove a result in the spirit of their work which is of a simpler form
and easier to apply. All results are true in the more general setting
of Musielak-Orlicz spaces.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 46B09, 46B07, 46B45, 60B99
Submitted from: joscha.prochno at jku.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.1442
or
http://arXiv.org/abs/1305.1442
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Yousef estaremi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:18:29 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "multiplication conditional
expectation type operators on Orlicz" by Yousef estaremi.
Abstract: In this paper we consider a generalized conditional-type Holder-
inequality and investigate some classic properties of multiplication
conditional expectation type operators on Orlicz-spaces.
Archive classification: math.FA
Remarks: 12 pages
Submitted from: estaremi at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.2481
or
http://arXiv.org/abs/1305.2481
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michael Dymond and Olga Maleva
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:19:52 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Differentiability inside sets
with upper Minkowski dimension one" by Michael Dymond and Olga Maleva.
Abstract: We show that every finite-dimensional Euclidean space contains
compact universal differentiability sets of upper Minkowski dimension
one. In other words, there are compact sets $S$ of upper Minkowski
dimension one such that every Lipschitz function defined on the whole
space is differentiable inside $S$. Such sets are constructed explicitly.
Archive classification: math.FA
Mathematics Subject Classification: 46T20
Remarks: 23 pages
Submitted from: o.maleva at bham.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.3154
or
http://arXiv.org/abs/1305.3154
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Costas Poulios and Athanasios Tsarpalias
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:21:31 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some combinatorial principles
for trees and applications to tree-families in Banach spaces" by Costas
Poulios and Athanasios Tsarpalias.
Abstract: Suppose that $(x_s)_{s\in S}$ is a normalized family in a
Banach space indexed by the dyadic tree $S$. Using Stern's combinatorial
theorem we extend important results from sequences in Banach spaces to
tree-families. More precisely, assuming that for any infinite chain
$\beta$ of $S$ the sequence $(x_s)_{s\in\beta}$ is weakly null, we
prove that there exists a subtree $T$ of $S$ such that for any infinite
chain $\beta$ of $T$ the sequence $(x_s)_{s\in\beta}$ is nearly (resp.,
convexly) unconditional. In the case where $(f_s)_{s\in S}$ is a family
of continuous functions, under some additional assumptions, we prove the
existence of a subtree $T$ of $S$ such that for any infinite chain $\beta$
of $T$, the sequence $(f_s)_{s\in\beta}$ is unconditional. Finally, in
the more general setting where for any chain $\beta$, $(x_s)_{s\in\beta}$
is a Schauder basic sequence, we obtain a dichotomy result concerning
the semi-boundedly completeness of the sequences $(x_s)_{s\in\beta}$.
Archive classification: math.FA
Mathematics Subject Classification: 05D10, 46B15
Submitted from: k-poulios at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.4186
or
http://arXiv.org/abs/1305.4186
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Diana Marcela Serrano-Rodriguez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:23:22 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Absolutely \gamma-summing
multilinear operators" by Diana Marcela Serrano-Rodriguez.
Abstract: In this paper we introduce an abstract approach to the notion of
absolutely summing multilinear operators. We show that several previous
results on different contexts (absolutely summing, almost summing,
Cohen summing) are particular cases of our general results.
Archive classification: math.FA
Submitted from: dmserrano0 at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.4626
or
http://arXiv.org/abs/1305.4626
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jan van Neerven
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:27:57 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Compactness in the Lebesgue-Bochner
spaces L^p(\mu;X)" by Jan van Neerven.
Abstract: Let (\Omega,\mu) be a finite measure space, X a Banach space,
and let 1\le p<\infty. The aim of this paper is to give an elementary
proof of the Diaz--Mayoral theorem that a subset V of L^p(\mu;X)
is relatively compact if and only if it is uniformly p-integrable,
uniformly tight, and scalarly relatively compact.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46E40, Secondary: 46E30,
46B50
Remarks: 5 pages, submitted for publication
Submitted from: J.M.A.M.vanNeerven at tudelft.nl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.5688
or
http://arXiv.org/abs/1305.5688
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jameson Cahill, Peter G. Casazza, Jesse
Peterson and Lindsey
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:30:00 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Real phase retrieval by
projections" by Jameson Cahill, Peter G. Casazza, Jesse Peterson and
Lindsey.
Abstract: The problem of recovering a vector from the absolute values
of its inner products against a family of measurement vectors has been
well studied in mathematics and engineering. A generalization of this
phase retrieval problem also exists in engineering: recovering a vector
from measurements consisting of norms of its orthogonal projections onto
a family of subspaces. There exist semidefinite programming algorithms
to solve this problem, but much remains unknown for this more general
case. Can families of subspaces for which such measurements are injective
be completely classified? What is the minimal number of subspaces required
to have injectivity? How closely does this problem compare to the usual
phase retrieval problem with families of measurement vectors? In this
paper, we answer or make incremental steps toward these questions. We
provide several characterizations of subspaces which yield injective
measurements, and through a concrete construction, we prove the surprising
result that phase retrieval can be achieved with $2M-1$ projections of
arbitrary rank in $\HH_M$.
Finally we present several open problems as we discuss issues unique to
the phase retrieval problem with subspaces.
Archive classification: math.FA
Submitted from: lmwvh4 at mail.missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.6226
or
http://arXiv.org/abs/1305.6226
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kobos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:31:34 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Equilateral dimension of some
classes of normed spaces" by Tomasz Kobos.
Abstract: An equilateral dimension of a normed space is a maximal number
of pairwise equidistant points of this space. The aim of this paper is to
study the equilateral dimension of certain classes of finite dimensional
normed spaces. The well-known conjecture states that the equilateral
dimension of any $n$-dimensional normed space is not less than $n+1$. By
using an elementary continuity argument, we establish it in the following
classes of spaces: permutation-invariant spaces, Orlicz-Musielak spaces
and in one codimensional subspaces of $\ell^n_{\infty}$. For smooth
and symmetric spaces, Orlicz-Musielak spaces satisfying an additional
condition and every $(n-1)$-dimensional subspace of $\ell^{n}_{\infty}$
we also provide some weaker bounds on the equilateral dimension for every
space which is sufficiently close to one of these. This generalizes the
result of Swanepoel and Villa concerning the $\ell_p^n$ spaces.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 46B85, 46B20, 52C17, 52A15, 52A20
Remarks: 12 pages
Submitted from: tkobos at wp.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.6288
or
http://arXiv.org/abs/1305.6288
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Richard Aron, Yun Sung Choi, Sun Kwang Kim,
Han Ju Lee, and Miguel Martin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:36:13 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Bishop-Phelps-Bollob\'as
version of Lindenstrauss properties A" by Richard Aron, Yun Sung Choi,
Sun Kwang Kim, Han Ju Lee, and Miguel Martin.
Abstract: We study a Bishop-Phelps-Bollob\'as version of Lindenstrauss
properties A and B. For domain spaces, we study Banach spaces $X$
such that $(X,Y)$ has the Bishop-Phelps-Bollob\'as property (BPBp)
for every Banach space $Y$. We show that in this case, there exists
a universal function $\eta_X(\eps)$ such that for every $Y$, the pair
$(X,Y)$ has the BPBp with this function. This allows us to prove some
necessary isometric conditions for $X$ to have the property. We also
prove that if $X$ has this property in every equivalent norm, then $X$
is one-dimensional. For range spaces, we study Banach spaces $Y$ such
that $(X,Y)$ has the Bishop-Phelps-Bollob\'as property for every Banach
space $X$. In this case, we show that there is a universal function
$\eta_Y(\eps)$ such that for every $X$, the pair $(X,Y)$ has the BPBp
with this function. This implies that this property of $Y$ is strictly
stronger than Lindenstrauss property B. The main tool to get these
results is the study of the Bishop-Phelps-Bollob\'as property for $c_0$-,
$\ell_1$- and $\ell_\infty$-sums of Banach spaces.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22
Submitted from: mmartins at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.6420
or
http://arXiv.org/abs/1305.6420
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by D. Freeman, E. Odell, B. Sari, and Th.
Schlumprecht
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:37:30 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Equilateral sets in uniformly
smooth Banach spaces" by D. Freeman, E. Odell, B. Sari, and
Th. Schlumprecht.
Abstract: Let $X$ be an infinite dimensional uniformly smooth Banach
space. We prove that $X$ contains an infinite equilateral set. That
is, there exists a constant $\lambda>0$ and an infinite sequence
$(x_i)_{i=1}^\infty\subset X$ such that $\|x_i-x_j\|=\lambda$ for all
$i\neq j$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B04
Remarks: 11 pages
Submitted from: dfreema7 at slu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.6750
or
http://arXiv.org/abs/1305.6750
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jamilson Ramos Campos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:38:40 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An abstract result on Cohen
strongly summing operators" by Jamilson Ramos Campos.
Abstract: We present an abstract result that characterizes the
coincidence of certain classes of linear operators with the class of
Cohen strongly summing linear operators. Our argument is extended
to multilinear operators and, as a consequence, we establish a few
alternative characterizations for the class of Cohen strongly summing
multilinear operators.
Archive classification: math.FA
Remarks: 9 pages
Submitted from: jamilson at dce.ufpb.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1305.7276
or
http://arXiv.org/abs/1305.7276
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Apostolos Giannopoulos, Pantelis
Stavrakakis, Antonis Tsolomitis and Beatrice-Helen Vritsiou
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:40:05 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Geometry of the $L_q$-centroid
bodies of an isotropic log-concave measure" by Apostolos Giannopoulos,
Pantelis Stavrakakis, Antonis Tsolomitis and Beatrice-Helen Vritsiou.
Abstract: We study some geometric properties of the $L_q$-centroid
bodies $Z_q(\mu )$ of an isotropic log-concave measure $\mu $ on
${\mathbb R}^n$. For any $2\ls q\ls\sqrt{n}$ and for $\varepsilon
\in (\varepsilon_0(q,n),1)$ we determine the inradius of a random
$(1-\varepsilon )n$-dimensional projection of $Z_q(\mu )$ up to a constant
depending polynomially on $\varepsilon $. Using this fact we obtain
estimates for the covering numbers $N(\sqrt{\smash[b]{q}}B_2^n,tZ_q(\mu
))$, $t\gr 1$, thus showing that $Z_q(\mu )$ is a $\beta $-regular convex
body. As a consequence, we also get an upper bound for $M(Z_q(\mu ))$.
Archive classification: math.FA math.MG
Submitted from: apgiannop at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1306.0246
or
http://arXiv.org/abs/1306.0246
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Denis Potapov and Fedor Sukochev
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:41:15 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Frechet differentiability of Sp
norms" by Denis Potapov and Fedor Sukochev.
Abstract: One of the long standing questions in the theory of Schatten-von
Neumann ideals of compact operators is whether their norms have the
same differentiability properties as the norms of their commutative
counterparts. We answer this question in the affirmative. A key technical
observation underlying our proof is a discovery of connection between
this question and recent affirmative resolution of L.S. Koplienko's
conjecture concerning existence of higher order spectral shift functions.
Archive classification: math.FA
Submitted from: d.potapov at unsw.edu.au
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1306.0362
or
http://arXiv.org/abs/1306.0362
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Miguel Martin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Jun 2013 14:42:29 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Norm-attaining compact operators"
by Miguel Martin.
Abstract: We show examples of compact linear operators between Banach
spaces which cannot be approximated by norm attaining operators. This is
the negative answer to an open question posed in the 1970's. Actually,
any strictly convex Banach space failing the approximation property
serves as the range space. On the other hand, there are examples in
which the domain space has Schauder basis. It now makes sense to discuss
sufficient conditions on the domain or the range space to ensure that
every compact linear operator between them can be approximated by norm
attaining operators. We get several basic results in this line and
mention some open problems.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46B04,
46B45, 46B28, 47B07
Submitted from: mmartins at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1306.1155
or
http://arXiv.org/abs/1306.1155
Return-path: <alspach at math.okstate.edu>
From: James Lacey <james.lacey at att.net>
Reply-to: James Lacey <james.lacey at att.net>
To: "banach at cauchy.math.okstate.edu" <banach at cauchy.math.okstate.edu>
Date: Fri, Jun 21, 2013 at 6:44 PM
Subject: [Banach] Dr. Howard Elton Lacey
Just wanted to let the list know that my father Dr. Elton Lacey who was
a Banach space researcher passed away today after a lengthy illness. Some
of you may have known of him at the least.
I have included a short summary of his life below. Thank you and best of
luck to you all in your endeavors.
Elton graduated from Leakey High School in 1955 and entered Texas A&M
Univ. shortly thereafter. In the summer of 1957 he worked with the Corps
of Engineers on the Mississippi river cutting transit lines for flood
control projects. The first day there he went to the 4th St. Church
of Christ and met his future wife Bonnie Brown and they were married
August 1958 in Natchez, MS. That fall Elton continued his education at
Abilene Christian Univ. where he received his B.A. in Mathematics in 1959
and his M.A. in Mathematics in 1960. Next Elton and Bonnie moved their
family to Las Cruses, NM where Elton attended New Mexico State Univ. and
earned his Ph.D. in Mathematics in 1963. In the summer of 1963 Elton
worked at White Sands Missile Range in NM. That fall he returned to ACU
as Assistant Professor. In the summer of 1964 he went to UT at Austin
as an Asst. Professor. He was promoted to Assoc. Prof. in 1969 and
full Prof. in 1974. He took leave from UT twice during his tenure. In
the summer of 1966 and during the academic year of 1967-1968 Elton was
at the Analysis Division of the Manned Space Craft Center. During the
academic year of 1972-1973 Elton was at the Institute of Mathematics,
Polish Academy of Science in Warsaw. While there Elton wrote letters
home describing our experiences in Poland. His Aunt Cindy kept them and
they were later typed up and turned into a family book. In 1974 he was
promoted to Professor at UT Austin. When Dr. R. H. Bing returned to UT
as Chairmen of Mathematics, Elton served as his Vice-Chairman. A number
of his publications while at UT were with S. J. Bernau in Functional
Analysis and Banach Spaces. He also published a book with Springer-Verlag,
Berlin, NY in their prestigious Yellow Series, and another with UT Press
and one with TAMU Press.
In the summer of 1980 Elton taught math at the Free Univ. of
Berlin, W. Germany. When he returned to Texas, he started as Prof. and
Head of Mathematics, Texas A&M Univ., 1980-91. He served at Texas A&M
Univ. from 1991-92 as Prof and Assoc. Dean. Later, he returned to his
first love, teaching mathematics and retired in 2002. Upon retiring he
was named a Prof. Emeritus of Mathematics.
In the early 1990s Elton and Bonnie started working on family history. He
was featured in the Dallas Morning News for using the internet for
genealogy. Elton became an expert in Lacey family history and published
several genealogy books including one on his maternal ancestors the Brices.
He was a member of a number of heritage societies including the Sons of the
American Revolution.
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Elton Lacey Funeral, Scholarship
From: Dale Alspach <alspach at szlenk.math.okstate.edu>
Date: Thu, 27 Jun 2013 10:41:56 -0500
To: banach at math.okstate.edu
http://www.legacy.com/obituaries/theeagle/obituary.aspx?n=howard-lacey-elton&pid=165546355#fbLoggedOut
is a link to a newspaper obituary for Elton Lacey. It also gives details
about
the funeral. The family prefers donations to a scholarship fund rather than
sending flowers. A link to a donation page is provided.
Dale Alspach
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Date: Sat, 29 Jun 2013 16:31:39 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Niushan Gao and Foivos Xanthos
This is an announcement for the paper "Unbounded order convergence
and application to martingales without probability" by Niushan Gao and
Foivos Xanthos.
Abstract: A net $(x_\alpha)_{\alpha\in \Gamma}$ in a vector lattice $X$
is unbounded order convergent (uo-convergent) to $x$ if $|x_\alpha-x|
\wedge y \xrightarrow{{o}} 0$ for each $y \in X_+$, and is unbounded
order Cauchy (uo-Cauchy) if the net $(x_\alpha-x_{\alpha'})_{\Gamma\times
\Gamma}$ is uo-convergent to $0$. In the first part of this article,
we study uo-convergent and uo-Cauchy nets in Banach lattices and use
them to characterize Banach lattices with the positive Schur property and
KB-spaces. In the second part, we use the concept of uo-Cauchy sequences
to extend Doob's submartingale convergence theorems to a measure-free
setting. Our results imply, in particular, that every norm bounded
submartingale in $L_1(\Omega;F)$ is almost surely uo-Cauchy in $F$,
where $F$ is an order continuous Banach lattice with a weak unit.
Archive classification: math.FA
Submitted from: foivos at ualberta.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1306.2563
or
http://arXiv.org/abs/1306.2563
Return-path: <alspach at math.okstate.edu>
Date: Sat, 29 Jun 2013 16:36:43 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Adam Marcus, Daniel A Spielman, and Nikhil
Srivastava
This is an announcement for the paper "Interlacing families II: Mixed
characteristic polynomials and a question of Kadison and Singer" by Adam
Marcus, Daniel A Spielman, and Nikhil Srivastava.
Abstract: We use the method of interlacing families of polynomials
to prove Weaver's conjecture KS_2, which is known to imply a positive
answer to a famous question of Kadison and Singer via Anderson's Paving
Conjecture. Our proof goes through an analysis of the largest roots of a
family of polynomials that we call the "mixed characteristic polynomials"
of a collection of matrices.
Archive classification: math.CO math.FA math.OA
Submitted from: spielman at cs.yale.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1306.3969
or
http://arXiv.org/abs/1306.3969
Return-path: <alspach at math.okstate.edu>
Date: Sat, 29 Jun 2013 16:41:12 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Gilles Pisier
This is an announcement for the paper "On the metric entropy of the
Banach-Mazur compactum" by Gilles Pisier.
Abstract: We study of the metric entropy of the metric space $\cl B_n$ of
all $n$-dimensional Banach spaces (the so-called Banach-Mazur compactum)
equipped with the Banach-Mazur (multiplicative) ``distance" $d$. We
are interested either in estimates independent of the dimension or in
asymptotic estimates when the dimension tends to $\infty$. For instance,
we prove that, if $N({\cl B_n},d, 1+\vp)$ is the smallest number of
``balls" of ``radius" $1+\vp$ that cover $\cl B_n$, then for any $\vp>0$
we have $$0<\liminf_{n\to \infty} \log\log N(\cl B_n,d,1+\vp)\le
\limsup_{n\to \infty} \log\log N(\cl B_n,d,1+\vp)<\infty.$$ We also
prove similar results for the matricial operator space analogues.
Archive classification: math.FA
Submitted from: pisier at math.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1306.5325
or
http://arXiv.org/abs/1306.5325
Return-path: <alspach at math.okstate.edu>
Date: Sat, 29 Jun 2013 16:43:13 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Mikhail I. Ostrovskii
This is an announcement for the paper "Radon-Nikod\'ym property and
thick families of geodesics" by Mikhail I. Ostrovskii.
Abstract: Banach spaces without the Radon-Nikod\'ym property are
characterized as spaces containing bilipschitz images of thick families of
geodesics defined as follows. A family $T$ of geodesics joining points $u$
and $v$ in a metric space is called {\it thick} if there is $\alpha>0$
such that for every $g\in T$ and for any finite collection of points
$r_1,\dots,r_n$ in the image of $g$, there is another $uv$-geodesic
$\widetilde g\in T$ satisfying the conditions: $\widetilde g$ also
passes through $r_1,\dots,r_n$, and, possibly, has some more common
points with $g$. On the other hand, there is a finite collection of
common points of $g$ and $\widetilde g$ which contains $r_1,\dots,r_n$
and is such that the sum of maximal deviations of the geodesics between
these common points is at least $\alpha$.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B22, 46B85, 54E35
Submitted from: ostrovsm at stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1306.5807
or
http://arXiv.org/abs/1306.5807
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] SUMIRFAS
From: Bill Johnson <johnson at math.tamu.edu>
Date: Mon, 1 Jul 2013 17:09:14 -0500 (CDT)
To: banach at math.okstate.edu
1st ANNOUNCEMENT OF SUMIRFAS 2013
The Informal Regional Functional Analysis Seminar
August 2-4
Texas A&M University, College Station
Schedule: Talks for SUMIRFAS will be posted on the Workshop in Analysis
and Probability page, whose URL is
http://www.math.tamu.edu/~kerr/workshop/
The first talk will be in the early afternoon on Friday and the Seminar
concludes by lunch time on Sunday. All talks will be in Blocker 169. The
Blocker Building is on Ireland St. just south of University Dr. on the
Texas A&M campus:
http://www.math.tamu.edu/contact/blocker.html.
Coffee and refreshments will be available in Blocker 148.
SUMIRFAS 2013 is dedicated to the memory of Ted Odell, who was one of the
organizers of the UTAMIRFAS, the predecessor of SUMIRFAS. Ted served with
distinction on the advisory board of the Workshop from its beginning until
his untimely passing in January.
The Plenary speakers at SUMIRFAS 2013 are Stephen Dilworth, Steve Jackson,
Masoud Khalkhali, Thomas Schlumprecht, Nicole Tomczak-Jaegermann, and
Wilhelm Winter. Other speakers include Tim Rainone, Paul Skoufranis, and
John Williams.
August 5-9 there will be a Concentration Week on "Dynamics, Geometry, and
Operator Algebras", organized by David Kerr and Guoliang Yu. This
Concentration Week aims to promote connections between nuclearity, nuclear
dimension, group C*-algebras and crossed products, topological and
measurable dynamics, algebraic dynamics, entropy, dimensional ideas from
coarse geometry, and K-theory with applications to topology. The program
will feature lecture series by David Kerr, Stuart White, and Rufus
Willett. The URL for this Concentration Week is
http://www.math.tamu.edu/~kerr/concweek13/
Immediately preceding SUMIRFAS, on August 1, there will be a celebration
of "The Mathematical Legacy of Ted Odell", organized by Thomas
Schlumprecht. The URL for this activity is
http://math.slu.edu/~freeman/LegacyConference/
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>. For more information on the Workshop
itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr
<kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>.
For information about the Concentration Week on "Dynamics, Geometry, and
Operator Algebras" contact David Kerr <kerr at math.tamu.edu>.
For information about the day devoted to "The Mathematical Legacy of Ted
Odell" contact Thomas Schlumprecht <schlump at math.tamu.edu>
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
From banach-bounces at math.okstate.edu Sat Jul 20 14:26:45 2013
Date: Sat, 20 Jul 2013 12:48:12 -0500 (CDT)
From: Bill Johnson <johnson at math.tamu.edu>
To: banach at math.okstate.edu
Subject: [Banach] SUMIRFAS Schedule
Please see the URL below for the schedule for SUMIRFAS, August 2-4, 2013, at Texas
A&M University.
Bill Johnson
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_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Maria Acosta, Julio Becerra, Yun Sung Choi,
Maciej Ciesielski, Sun Kwang Kim, Han Ju Lee, and Miguel Martin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Jul 2013 09:28:57 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Bishop-Phelps-Bollob\'as
property for operators between spaces of continuous functions" by Maria
Acosta, Julio Becerra, Yun Sung Choi, Maciej Ciesielski, Sun Kwang Kim,
Han Ju Lee, and Miguel Martin.
Abstract: We show that the space of bounded and linear operators between
spaces of continuous functions on compact Hausdorff topological spaces
has the Bishop-Phelps-Bollob\'as property. A similar result is also
proved for the class of compact operators from the space of continuous
functions vanishing at infinity on a locally compact and Hausdorff
topological space into a uniformly convex space, and for the class of
compact operators from a Banach space into a predual of an $L_1$-space.
Archive classification: math.FA
Mathematics Subject Classification: 46B04
Submitted from: mmartins at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1306.6740
or
http://arXiv.org/abs/1306.6740
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Aude Dalet
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Jul 2013 09:34:05 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Free spaces over countable compact
metric spaces" by Aude Dalet.
Abstract: We prove that the Lipschitz-free space over a countable
compact metric space is isometric to a dual space and has the metric
approximation property.
Archive classification: math.FA
Submitted from: aude.dalet at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.0735
or
http://arXiv.org/abs/1307.0735
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Cariello and Juan B.
Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Jul 2013 09:35:34 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Basic sequences and spaceability
in $\ell_p$ spaces" by Daniel Cariello and Juan B. Seoane-Sepulveda.
Abstract: Let $X$ be a sequence space and denote by $Z(X)$ the
subset of $X$ formed by sequences having only a finite number of
zero coordinates. We study algebraic properties of $Z(X)$ and show
(among other results) that (for $p \in [1,\infty]$) $Z(\ell_p)$ does
not contain infinite dimensional closed subspaces. This solves an open
question originally posed by R. M. Aron and V. I. Gurariy in 2003 on
the linear structure of $Z(\ell_\infty)$.
In addition to this, we also give a thorough analysis of the existing
algebraic structures within the set $X \setminus Z(X)$ and its algebraic
genericity.
Archive classification: math.FA
Remarks: 17 pages
Submitted from: jseoane at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.2508
or
http://arXiv.org/abs/1307.2508
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikael de la Salle
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Jul 2013 09:39:25 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Towards Banach space strong
property (T) for SL(3,R)" by Mikael de la Salle.
Abstract: We prove that SL(3,R) has strong property (T) in Lafforgue's
sense with respect to the Banach spaces that are \theta>0 interpolation
spaces (for the Lions-Calder\'on complex interpolation method) between
an arbitrary Banach space and a Banach space with sufficiently
good type and cotype. As a consequence, for such a Banach space
X, SL(3,R) and its lattices have the fixed point property (F_X) of
Bader--Furman--Gelander--Monod, and the expanders contructed from SL(3,Z)
do not admit a coarse embedding into X. We also prove a quantitative
decay of matrix coefficients (Howe-Moore property) for representations
with small exponential growth of SL(3,R) on X.
This class of Banach spaces contains the classical superreflexive spaces
and some nonreflexive spaces as well. We see no obstruction for this
class to be equal to all spaces with nontrivial type.
Archive classification: math.GR math.FA math.MG
Remarks: 31 pages, 3 figures. Comments welcome!
Submitted from: delasall at phare.normalesup.org
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.2475
or
http://arXiv.org/abs/1307.2475
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Susanna Dann
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Jul 2013 09:41:06 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Intersection bodies with certain
symmetries" by Susanna Dann.
Abstract: We generalize the class of intersection bodies in $\R^n$
by imposing invariance under a certain subgroup of orthogonal
transformations. We show that this class of bodies shares many properties
with their real counterparts.
Archive classification: math.FA
Submitted from: danns at missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.3206
or
http://arXiv.org/abs/1307.3206
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Simon Lucking
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Jul 2013 09:42:53 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The almost Daugavet property and
translation-invariant subspaces" by Simon Lucking.
Abstract: Let $G$ be a metrizable, compact abelian group and let $\Lambda$
be a subset of its dual group $\widehat G$. We show that $C_\Lambda(G)$
has the almost Daugavet property if and only if $\Lambda$ is an infinite
set, and that $L^1_\Lambda(G)$ has the almost Daugavet property if and
only if $\Lambda$ is not a $\Lambda(1)$ set.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 43A46
Remarks: 12 pages
Submitted from: simon.luecking at fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.3629
or
http://arXiv.org/abs/1307.3629
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jesus M. F. Castillo and Felix Cabello
Sanchez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Jul 2013 09:45:16 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Stability constants and the
homology of quasi-Banach spaces" by Jesus M. F. Castillo and Felix
Cabello Sanchez.
Abstract: We affirmatively solve the main problems posed by Laczkovich
and Paulin in \emph{Stability constants in linear spaces}, Constructive
Approximation 34 (2011) 89--106 (do there exist cases in which the
second Whitney constant is finite while the approximation constant is
infinite?) and by Cabello and Castillo in \emph{The long homology sequence
for quasi-Banach spaces, with applications}, Positivity 8 (2004) 379--394
(do there exist Banach spaces $X,Y$ for which $\Ext(X,Y)$ is Hausdorff
and non-zero?). In fact, we show that these two problems are the same.
Archive classification: math.FA
Remarks: This paper is to appear in Israel Journal of Mathematics
Submitted from: castillo at unex.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.4382
or
http://arXiv.org/abs/1307.4382
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jesus M.F. Castillo, and Yolanda Moreno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Jul 2013 09:47:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the bounded approximation
property in Banach spaces" by Jesus M.F. Castillo, and Yolanda Moreno.
Abstract: We prove that the kernel of a quotient operator from
an $\mathcal L_1$-space onto a Banach space $X$ with the Bounded
Approximation Property (BAP) has the BAP. This completes earlier results
of Lusky --case $\ell_1$-- and Figiel, Johnson and Pe\l czy\'nski --case
$X^*$ separable. Given a Banach space $X$, we show that if the kernel of
a quotient map from some $\mathcal L_1$-space onto $X$ has the BAP then
every kernel of every quotient map from any $\mathcal L_1$-space onto $X$
has the BAP. The dual result for $\mathcal L_\infty$-spaces also hold:
if for some $\mathcal L_\infty$-space $E$ some quotient $E/X$ has the
BAP then for every $\mathcal L_\infty$-space $E$ every quotient $E/X$
has the BAP.
Archive classification: math.FA
Remarks: To appear in Israel Journal of Mathematics
Submitted from: castillo at unex.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.4383
or
http://arXiv.org/abs/1307.4383
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jesus M. F. Castillo, Pier Luigi Papini and
Marilda A. Simoes
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Jul 2013 09:50:29 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Thick coverings for the unit
ball of a Banach space" by Jesus M. F. Castillo, Pier Luigi Papini and
Marilda A. Simoes.
Abstract: We study the behaviour of Whitley's thickness constant of a
Banach space with respect to $\ell_p$-products and we compute it for
classical $L_p$-spaces.
Archive classification: math.FA
Remarks: This paper is to appear in Houston Journal of Mathematics
Submitted from: castillo at unex.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.4385
or
http://arXiv.org/abs/1307.4385
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jesus M. F. Castillo, Valentin Ferenczi and
Yolanda Moreno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Jul 2013 09:53:01 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On uniformly finitely extensible
Banach spaces" by Jesus M. F. Castillo, Valentin Ferenczi and Yolanda
Moreno.
Abstract: We continue the study of Uniformly Finitely Extensible Banach
spaces (in short, UFO) initiated in Moreno-Plichko, \emph{On automorphic
Banach spaces}, Israel J. Math. 169 (2009) 29--45 and Castillo-Plichko,
\emph{Banach spaces in various positions.} J. Funct. Anal. 259 (2010)
2098-2138. We show that they have the Uniform Approximation Property
of Pe\l czy\'nski and Rosenthal and are compactly extensible. We will
also consider their connection with the automorphic space problem of
Lindenstrauss and Rosenthal --do there exist automorphic spaces other than
$c_0(I)$ and $\ell_2(I)$?-- showing that a space all whose subspaces are
UFO must be automorphic when it is Hereditarily Indecomposable (HI),
and a Hilbert space when it is either locally minimal or isomorphic
to its square. We will finally show that most HI --among them, the
super-reflexive HI space constructed by Ferenczi-- and asymptotically
$\ell_2$ spaces in the literature cannot be automorphic.
Archive classification: math.FA
Remarks: This paper is to appear in the Journal of Mathematical
Analysis and
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.4386
or
http://arXiv.org/abs/1307.4386
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio Aviles, Felix Cabello Sanchez,
Jesus M. F. Castillo, Manuel Gonzalez and Yolanda Moreno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Jul 2013 09:58:05 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On ultrapowers of Banach spaces
of type $\mathscr L_\infty$" by Antonio Aviles, Felix Cabello Sanchez,
Jesus M. F. Castillo, Manuel Gonzalez and Yolanda Moreno.
Abstract: We prove that no ultraproduct of Banach spaces via a countably
incomplete ultrafilter can contain $c_0$ complemented. This shows that
a ``result'' widely used in the theory of ultraproducts is wrong. We
then amend a number of results whose proofs had been infected by that
statement. In particular we provide proofs for the following statements:
(i) All $M$-spaces, in particular all $C(K)$-spaces, have ultrapowers
isomorphic to ultrapowers of $c_0$, as well as all their complemented
subspaces isomorphic to their square. (ii) No ultrapower of the Gurari\u
\i\ space can be complemented in any $M$-space. (iii) There exist Banach
spaces not complemented in any $C(K)$-space having ultrapowers isomorphic
to a $C(K)$-space.
Archive classification: math.FA
Remarks: This paper is to appear in Fundamenta Mathematica
Submitted from: castillo at unex.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.4387
or
http://arXiv.org/abs/1307.4387
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Pellegrino and Juan B.
Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Jul 2013 09:59:52 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Grothendieck's theorem for
absolutely summing multilinear operators is optimal" by Daniel
Pellegrino and Juan B. Seoane-Sepulveda.
Abstract: Grothendieck's theorem asserts that every continuous
linear operator from $\ell_{1}$ to $\ell_{2}$ is absolutely $\left(
1;1\right) $-summing. In this note we prove that the optimal
constant $g_{m}$ so that every continuous $m$-linear operator from
$\ell_{1}\times\cdots\times\ell_{1}$ to $\ell_{2}$ is absolutely
$\left(g_{m};1\right) $-summing is $\frac{2}{m+1}$. This result solves
(in the positive) a conjecture posed by A.T. Bernardino in 2011.
Archive classification: math.FA
Submitted from: pellegrino at pq.cnpq.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.4809
or
http://arXiv.org/abs/1307.4809
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Umut Caglar and Elisabeth M. Werner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Jul 2013 10:01:10 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Divergence for s-concave and log
concave functions" by Umut Caglar and Elisabeth M. Werner.
Abstract: We prove new entropy inequalities for log concave and s-concave
functions that strengthen and generalize recently established reverse log
Sobolev and Poincare inequalities for such functions. This leads naturally
to the concept of f-divergence and, in particular, relative entropy for
s-concave and log concave functions. We establish their basic properties,
among them the affine invariant valuation property. Applications are
given in the theory of convex bodies.
Archive classification: math.FA
Submitted from: elisabeth.werner at case.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.5409
or
http://arXiv.org/abs/1307.5409
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Manuel D. Contreras, Santiago
Diaz-Madrigal, and Dragan Vukotic
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Jul 2013 10:02:44 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Compact and weakly compact
composition operators from the Bloch space into M\"obius invariant spaces"
by Manuel D. Contreras, Santiago Diaz-Madrigal, and Dragan Vukotic.
Abstract: We obtain exhaustive results and treat in a unified way the
question of boundedness, compactness, and weak compactness of composition
operators from the Bloch space into any space from a large family of
conformally invariant spaces that includes the classical spaces like
$BMOA$, $Q_\alpha$, and analytic Besov spaces $B^p$. In particular, by
combining techniques from both complex and functional analysis, we prove
that in this setting weak compactness is equivalent to compactness. For
the operators into the corresponding ``small'' spaces we also characterize
the boundedness and show that it is equivalent to compactness.
Archive classification: math.FA
Mathematics Subject Classification: 47B33
Submitted from: dragan.vukotic at uam.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.5784
or
http://arXiv.org/abs/1307.5784
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Charles John Read
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Aug 2013 12:54:11 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Banach spaces with no proximinal
subspaces of codimension 2" by Charles John Read.
Abstract: The classical theorem of Bishop-Phelps asserts that, for a
Banach space X, the norm-achieving functionals in X* are dense in X*. Bela
Bollobas's extension of the theorem gives a quantitative description of
just how dense the norm-achieving functionals have to be: if (x,f) is
in X x X* with ||x||=||f||=1 and |1-f(x)|< h^2/4 then there are (x',f')
in X x X* with ||x'||= ||f'||=1, ||x-x'||, ||f-f'||< h and f'(x')=1.
This means that there are always "proximinal" hyperplanes H in X
(a nonempty subset E of a metric space is said to be "proximinal" if,
for x not in E, the distance d(x,E) is always achieved - there is always
an e in E with d(x,E)=d(x,e)); for if H= ker f (f in X*) then it is easy
to see that H is proximinal if and only if f is norm-achieving. Indeed
the set of proximinal hyperplanes H is, in the appropriate sense, dense
in the set of all closed hyperplanes H in X.
Quite a long time ago [Problem 2.1 in his monograph "The Theory of Best
approximation and Functional Analysis" Regional Conference series in
Applied Mathematics, SIAM, 1974], Ivan Singer asked if this result
generalized to closed subspaces of finite codimension - if every Banach
space has a proximinal subspace of codimension 2, for example. In
this paper I show that there is a Banach space X such that X has no
proximinal subspace of finite codimension n>1. So we have a converse to
Bishop-Phelps-Bollobas: a dense set of proximinal hyperplanes can always
be found, but proximinal subspaces of larger, finite codimension need
not be.
Archive classification: math.FA
Mathematics Subject Classification: 46B04 (Primary), 46B45, 46B25
(Secondary)
Remarks: The paper has been submitted for publication to the Israel
Journal of
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.7958
or
http://arXiv.org/abs/1307.7958
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sonia Berrios and Geraldo Botelho
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Aug 2013 12:55:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A general abstract approach to
approximation properties in Banach" by Sonia Berrios and Geraldo Botelho.
Abstract: We propose a unifying approach to many approximation
properties studied in the literature from the 1930s up to our days. To
do so, we say that a Banach space E has the (I,J,{\tau})-approximation
property if E-valued operators belonging to the operator ideal I can
be approximated, with respect to the topology {\tau}, by operators
belonging to the operator ideal J. Restricting {\tau} to a class of linear
topologies, which we call ideal topologies, this concept recovers many
classical/recent approximation properties as particular instances and
several important known results are particular cases of more general
results that are valid in this abstract framework.
Archive classification: math.FA
Submitted from: botelho at ufu.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1307.8073
or
http://arXiv.org/abs/1307.8073
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Horst Martini, Pier Luigi Papini, and
Margarita Spirova
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Aug 2013 13:02:23 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Complete sets and completion
of sets in Banach spaces" by Horst Martini, Pier Luigi Papini, and
Margarita Spirova.
Abstract: In this paper we study properties of complete sets and
of completions of sets in Banach spaces. We consider the family of
completions of a given set and its size; we also study in detail the
relationships concerning diameters, radii, and centers. The results are
illustrated by several examples.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 46B20, 46B99, 52A05, 52A20, 52A21
Submitted from: margarita.spirova at mathematik.tu-chemnitz.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.0789
or
http://arXiv.org/abs/1308.0789
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sun Kwang Kim and Han Ju Lee
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Aug 2013 13:11:41 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Simultaneously continuous
retraction and its application" by Sun Kwang Kim and Han Ju Lee.
Abstract: We study the existence of a retraction from the dual space $X^*$
of a (real or complex) Banach space $X$ onto its unit ball $B_{X^*}$
which is uniformly continuous in norm topology and continuous in weak-$*$
topology. Such a retraction is called a uniformly simultaneously
continuous retraction.
It is shown that if $X$ has a normalized unconditional Schauder
basis with unconditional basis constant 1 and $X^*$ is uniformly monotone,
then a uniformly simultaneously continuous retraction from $X^*$ onto
$B_{X^*}$ exists. It is also shown that if $\{X_i\}$ is a family of
separable Banach spaces whose duals are uniformly convex with moduli
of convexity $\delta_i(\eps)$ such that $\inf_i \delta_i(\eps)>0$
and $X= \left[\bigoplus X_i\right]_{c_0}$ or $X=\left[\bigoplus
X_i\right]_{\ell_p}$ for $1\le p<\infty$, then a uniformly simultaneously
continuous retraction exists from $X^*$ onto $B_{X^*}$.
The relation between the existence of a uniformly simultaneously
continuous retraction and the Bishsop-Phelps-Bollob\'as property for
operators is investigated and it is proved that the existence of a
uniformly simultaneously continuous retraction from $X^*$ onto its unit
ball implies that a pair $(X, C_0(K))$ has the Bishop-Phelps-Bollob\'as
property for every locally compact Hausdorff spaces $K$. As a corollary,
we prove that $(C_0(S), C_0(K))$ has the Bishop-Phelps-Bollob\'as property
if $C_0(S)$ and $C_0(K)$ are the spaces of all real-valued continuous
functions vanishing at infinity on locally compact metric space $S$
and locally compact Hausdorff space $K$ respectively.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22
Remarks: 15 pages
Submitted from: hanjulee at dongguk.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.1638
or
http://arXiv.org/abs/1308.1638
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Marek Cuth and Ondrej F.K. Kalenda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Aug 2013 13:13:19 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Rich families and elementary
submodels" by Marek Cuth and Ondrej F.K. Kalenda.
Abstract: We compare two methods of proving separable reduction theorems
in functional analysis -- the method of rich families and the method of
elementary submodels. We show that any result proved using rich families
holds also when formulated with elementary submodels and the converse is
true in spaces with fundamental minimal system an in spaces of density
$\aleph_1$. We do not know whether the converse is true in general. We
apply our results to show that a projectional skeleton may be without
loss of generality indexed by ranges of its projections.
Archive classification: math.FA
Mathematics Subject Classification: 46B26, 03C30
Submitted from: cuthm5am at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.1818
or
http://arXiv.org/abs/1308.1818
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Enrico Boasso
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Aug 2013 13:19:09 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the Moore-Penrose inverse, EP
Banach space operators and EP Banach algebra elements" by Enrico Boasso.
Abstract: The main concern of this note is the Moore-Penrose inverse in
the context of Banach spaces and algebras. Especially attention will be
given to a particular class of elements with the aforementioned inverse,
namely EP Banach space operators and Banach algebra elements, which will
be studied and characterized extending well-known results obtained in
the frame of Hilbert space operators and $C^*$-algebra elements.
Archive classification: math.FA
Mathematics Subject Classification: Primary 15A09, Secondary 47A05
Citation: J. Math. Anal. Appl. 339(2) (2008), 1003-1014
Remarks: 20 pages, original research article
Submitted from: eboasso at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.1897
or
http://arXiv.org/abs/1308.1897
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ludek Zajicek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Aug 2013 13:22:42 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Properties of Hadamard directional
derivatives: Denjoy-Young-Saks theorem for functions on Banach spaces"
by Ludek Zajicek.
Abstract: The classical Denjoy-Young-Saks theorem on Dini derivatives
of arbitrary functions $f: \R \to \R$ was extended by U.S. Haslam-Jones
(1932) and A.J. Ward (1935) to arbitrary functions on $\R^2$. This
extension gives the strongest relation among upper and lower Hadamard
directional derivatives $f^+_H (x,v)$, $f^-_H (x,v)$ ($v \in X$) which
holds almost everywhere for an arbitrary function $f:\R^2\to \R$. Our
main result extends the theorem of Haslam-Jones and Ward to functions
on separable Banach spaces.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46G05, Secondary: 26B05
Submitted from: zajicek at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.2415
or
http://arXiv.org/abs/1308.2415
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alon Dmitriyuk and Yehoram Gordon
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Aug 2013 13:25:39 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Large distortion dimension
reduction using random variable" by Alon Dmitriyuk and Yehoram Gordon.
Abstract: Consider a random matrix
$H:\mathbb{R}^n\longrightarrow\mathbb{R}^m$. Let $D\geq2$ and let
$\{W_l\}_{l=1}^{p}$ be a set of $k$-dimensional affine subspaces of
$\mathbb{R}^n$. We ask what is the probability that for all $1\leq l\leq
p$ and $x,y\in W_l$,
\[ \|x-y\|_2\leq\|Hx-Hy\|_2\leq D\|x-y\|_2. \]
We show that for
$m=O\big(k+\frac{\ln{p}}{\ln{D}}\big)$ and a variety of different classes
of random matrices $H$, which include the class of Gaussian matrices,
existence is assured and the probability is very high. The estimate on
$m$ is tight in terms of $k,p,D$.
Archive classification: math.FA
Remarks: 18 pages
Submitted from: gordon at techunix.technion.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.2768
or
http://arXiv.org/abs/1308.2768
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Aug 2013 13:31:35 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Comparison of metric spectral gaps"
by Assaf Naor.
Abstract: Let $A=(a_{ij})\in M_n(\R)$ be an $n$ by $n$ symmetric
stochastic matrix. For $p\in [1,\infty)$ and a metric space $(X,d_X)$,
let $\gamma(A,d_X^p)$ be the infimum over those $\gamma\in (0,\infty]$
for which every $x_1,\ldots,x_n\in X$ satisfy
$$ \frac{1}{n^2} \sum_{i=1}^n\sum_{j=1}^n d_X(x_i,x_j)^p\le
\frac{\gamma}{n}\sum_{i=1}^n\sum_{j=1}^n a_{ij} d_X(x_i,x_j)^p.
$$
Thus $\gamma(A,d_X^p)$ measures the magnitude of the {\em nonlinear
spectral gap} of the matrix $A$ with
respect to the kernel $d_X^p:X\times X\to [0,\infty)$. We study pairs of
metric spaces $(X,d_X)$ and
$(Y,d_Y)$ for which there exists $\Psi:(0,\infty)\to (0,\infty)$
such that $\gamma(A,d_X^p)\le \Psi\left(\gamma(A,d_Y^p)\right)$ for
every symmetric
stochastic $A\in M_n(\R)$
with $\gamma(A,d_Y^p)<\infty$. When $\Psi$ is linear a complete
geometric
characterization is obtained.
Our estimates on nonlinear spectral gaps yield new embeddability results
as well as new nonembeddability results. For example, it is shown that
if $n\in \N$ and $p\in (2,\infty)$
then for every $f_1,\ldots,f_n\in L_p$ there exist $x_1,\ldots,x_n\in
L_2$
such that
\begin{equation}\label{eq:p factor} \forall\, i,j\in
\{1,\ldots,n\},\quad \|x_i-x_j\|_2\lesssim
p\|f_i-f_j\|_p,
\end{equation} and $$ \sum_{i=1}^n\sum_{j=1}^n
\|x_i-x_j\|_2^2=\sum_{i=1}^n\sum_{j=1}^n
\|f_i-f_j\|_p^2.
$$ This statement is impossible for $p\in [1,2)$, and the asymptotic
dependence on $p$ in~\eqref{eq:p factor}
is sharp. We also obtain the best known lower bound on the $L_p$
distortion of Ramanujan graphs,
improving over the work of Matou\v{s}ek. Links to
Bourgain--Milman--Wolfson type and a conjectural nonlinear Maurey--Pisier
theorem are studied.
Archive classification: math.MG math.FA
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.2851
or
http://arXiv.org/abs/1308.2851
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Petr Hajek and Thomas Schlumprecht
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Aug 2013 13:33:04 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Szlenk index of L_p(X)"
by Petr Hajek and Thomas Schlumprecht.
Abstract: We find an optimal upper bound on the values of the
weak$^*$-dentability index $Dz(X)$ in terms of the Szlenk index
$Sz(X)$ of a Banach space $X$ with separable dual. Namely,
if $\;Sz(X)=\omega^{\alpha}$, for some $\alpha<\omega_1$, and
$p\in(1,\infty)$, then
$$Sz(X)\le Dz(X)\le Sz(L_p(X))\le \begin{cases} \omega^{\alpha+1}
&\text{
if $\alpha$ is a finite ordinal,}
\omega^{\alpha} &\text{ if $\alpha$ is an infinite ordinal.}
\end{cases}$$
Archive classification: math.FA
Mathematics Subject Classification: 46B03 46B10
Submitted from: schlump at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.3629
or
http://arXiv.org/abs/1308.3629
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mirna Dzamonja
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Aug 2013 13:35:03 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Isomorphic universality and
the number of pairwise non-isomorphic in the class of Banach spaces"
by Mirna Dzamonja.
Abstract: We study isomorphic universality of Banach spaces of a given
density and a number of pairwise non-isomorphic models in the same
class. We show that in the Cohen model the isomorphic universality number
for Banach spaces of density $\aleph_1$ is $\aleph_2$, and analogous
results are true for other cardinals (Theorem 1.2(1)) and that adding
just one Cohen real to any model destroys the universality of Banach
spaces of density $\aleph_1$ (Theorem 1.5). We develop the framework
of natural spaces to study isomorphic embeddings of Banach spaces and
use it to show that a sufficient failure of the generalized continuum
hypothesis implies that the universality number of Banach spaces of a
given density under a certain kind of positive embeddings (very positive
embeddings), is high (Theorem 4.8(1)), and similarly for the number of
pairwise non-isomorphic models (Theorem 4.8(2)).
Archive classification: math.LO math.FA
Mathematics Subject Classification: 03E75, 46B26, 46B03, 03C45, 06E15
Submitted from: h020 at uea.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.3640
or
http://arXiv.org/abs/1308.3640
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Conference Announcement - 7th Conference on Function Spaces: May 2014
From: Krzysztof Jarosz <krzysztof.m.jarosz at gmail.com>
Date: Tue, 27 Aug 2013 14:32:01 -0500
To: banach at math.okstate.edu
7th Conference on Function Spaces will take place at the SIUE campus
between May 20 and May 24, 2014. The Conference will follow the same format
as the previous one:
http://www.siue.edu/MATH/conference2010/
If you consider attending the Conference it would help our preparation if
you could email us at kjarosz at siue.edu checking one of the following:
I will participate,
It is too early to decide, but I will likely come,
Keep me on the mailing list but chances of me coming are rather low
Comments:
Could you also pass this information to your colleagues and graduate
students?
We received a small grant to cover some of the local expenses but at this
point we are unable to offer any meaningful travel support. We are however
applying for an NSF grant to defer travel and local cost for "graduate
students, postdocs, young nontenured faculty, women and members of
underrepresented groups" (NSF priority) as well as for invited speakers.
Since the NSF founded the previous conferences in this series we are quite
hopeful that they will provide participants' support again.
Knowing well in advance the potential participants will increase chances
for an adequate support.
Sincerely yours,
Krzysztof Jarosz
Department of Mathematics and Statistics
Southern Illinois University Edwardsville
Edwardsville, IL 62026-1653, USA
tel.: (618) 650-2354
fax: (618) 650-3771
e-mail: kjarosz at siue.edu
http://www.siue.edu/~kjarosz/
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Deping Ye
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 30 Aug 2013 14:37:20 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the $L_p$ geominimal surface
area and related inequalities" by Deping Ye.
Abstract: In this paper, we introduce the $L_p$ Geominimal surface area
for all $-n\neq p<1$, which extends the classical Geominimal surface
area ($p=1$) by Petty and the $L_p$ Geominimal surface area by Lutwak
($p>1$). Our extension of the $L_p$ Geominimal surface area is motivated
by recent work on the extension of the $L_p$ affine surface area -- a
fundamental object in (affine) convex geometry. We prove some properties
for the $L_p$ Geominimal surface area and its related inequalities,
such as, the affine isoperimetric inequality and the Santal\'{o} style
inequality. Some cyclic inequalities are established to obtain the
monotonicity of the $L_p$ Geominimal surface area. Comparison between
the $L_p$ Geominimal surface area and the (formal) $p$-surface area is
also provided.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52A20, 53A15
Submitted from: deping.ye at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.4196
or
http://arXiv.org/abs/1308.4196
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Robert Bogucki
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 30 Aug 2013 14:38:39 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On explicit constructions of
auerbach bases in separable Banach spaces" by Robert Bogucki.
Abstract: This paper considers explicit constructions of Auerbach bases in
separable Banach spaces. Answering the question of A. Pe{\l}czy{\'n}ski,
we prove by construction the existence of Auerbach basis in arbitrary
subspace of $c_0$ of finite codimension and in the space $C(K)$ for $K$
compact countable metric space.
Archive classification: math.FA
Mathematics Subject Classification: 46B15, 46B20
Submitted from: r.bogucki at students.mimuw.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.4429
or
http://arXiv.org/abs/1308.4429
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Vincent Lafforgue and Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 30 Aug 2013 14:40:18 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A doubling subset of $L_p$ for
$p>2$ that is inherently infinite dimensional" by Vincent Lafforgue
and Assaf Naor.
Abstract: It is shown that for every $p\in (2,\infty)$ there exists a
doubling subset of $L_p$ that does not admit a bi-Lipschitz embedding
into $\R^k$ for any $k\in \N$.
Archive classification: math.MG math.FA
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.4554
or
http://arXiv.org/abs/1308.4554
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Markus Passenbrunner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 30 Aug 2013 14:41:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Unconditionality of orthogonal
spline systems in $L^p$" by Markus Passenbrunner.
Abstract: Given any natural number $k$ and any dense point sequence
$(t_n)$, we prove that the corresponding orthonormal spline system is
an unconditional basis in reflexive $L^p$.
Archive classification: math.FA
Remarks: 33 pages
Submitted from: markus.passenbrunner at jku.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.5055
or
http://arXiv.org/abs/1308.5055
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Miguel Lacruz and Luis Rodriguez-Piazza
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 30 Aug 2013 14:43:52 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Localizing algebras and invariant
subspaces" by Miguel Lacruz and Luis Rodriguez-Piazza.
Abstract: It is shown that the algebra \(L^\infty(\mu)\) of all
bounded measurable functions with respect to a finite measure \(\mu\)
is localizing on the Hilbert space \(L^2(\mu)\) if and only if
the measure \(\mu\) has an atom. Next, it is shown that the algebra
\(H^\infty({\mathbb D})\) of all bounded analytic multipliers on the unit
disc fails to be localizing, both on the Bergman space \(A^2({\mathbb
D})\) and on the Hardy space \(H^2({\mathbb D}).\) Then, several
conditions are provided for the algebra generated by a diagonal operator
on a Hilbert space to be localizing. Finally, a theorem is provided about
the existence of hyperinvariant subspaces for operators with a localizing
subspace of extended eigenoperators. This theorem extends and unifies
some previously known results of Scott Brown and Kim, Moore and Pearcy,
and Lomonosov, Radjavi and Troitsky.
Archive classification: math.OA
Mathematics Subject Classification: 47L10, 47A15
Remarks: 15 pages, submitted to J. Operator Theory
Submitted from: lacruz at us.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.4995
or
http://arXiv.org/abs/1308.4995
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Volker W. Thurey
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 30 Aug 2013 14:46:39 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The complex angle in normed spaces"
by Volker W. Thurey.
Abstract: We consider a generalized angle in complex normed vector
spaces. Its definition corresponds to the definition of the well known
Euclidean angle in real inner product spaces. Not surprisingly it yields
complex values as `angles'. This `angle' has some simple properties,
which are known from the usual angle in real inner product spaces. But
to do ordinary Euclidean geometry real angles are necessary. We show
that even in a complex normed space there are many pure real valued
`angles'. The situation improves yet in inner product spaces. There
we can use the known theory of orthogonal systems to find many pairs
of vectors with real angles, and to do geometry which is based on the
Greeks 2000 years ago.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46C05, 30E99
Remarks: 21 pages
Submitted from: volker at thuerey.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.5412
or
http://arXiv.org/abs/1308.5412
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ryan Causey
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 30 Aug 2013 14:50:12 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Estimation of the Szlenk index
of reflexive Banach spaces using generalized Baernstein spaces" by
Ryan Causey.
Abstract: For each ordinal $\alpha< \omega_1$, we prove the existence
of a separable, reflexive Banach space with a basis and Szlenk index
$\omega^{\alpha+1}$ which is universal for the class of separable,
reflexive Banach spaces $X$ such that the Szlenk indices $Sz(X), Sz(X^*)$
do not exceed $\omega^\alpha$.
Archive classification: math.FA
Submitted from: rcausey at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.5416
or
http://arXiv.org/abs/1308.5416
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Emanuel Milman and Liran Rotem
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 30 Aug 2013 14:52:09 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Complemented Brunn--Minkowski
inequalities and isoperimetry for homogeneous and non-homogeneous
measures" by Emanuel Milman and Liran Rotem.
Abstract: Elementary proofs of sharp isoperimetric inequalities on a
normed space $(\Real^n,\norm{\cdot})$ equipped with a measure $\mu
= w(x) dx$ so that $w^p$ is homogeneous are provided, along with a
characterization of the corresponding equality cases. When $p \in
(0,\infty]$ and in addition $w^p$ is assumed concave, the result is
an immediate corollary of the Borell--Brascamp--Lieb extension of
the classical Brunn--Minkowski inequality, providing an elementary
proof of a recent result of Cabr\'e--Ros Oton--Serra. When $p \in
(-1/n,0)$, the relevant property turns out to be a novel ``complemented
Brunn--Minkowski" inequality, which we show is always satisfied by $\mu$
when $w^p$ is homogeneous. This gives rise to a new class of measures,
which are ``complemented" analogues of the class of convex measures
introduced by Borell, but which have vastly different properties. The
resulting isoperimetric inequality and characterization of isoperimetric
minimizers extends beyond the recent results of Ca\~{n}ete--Rosales and
Howe. The isoperimetric and Brunn-Minkowski type inequalities extend to
the non-homogeneous setting, under a certain log-convexity assumption
on the density. Finally, we obtain functional, Sobolev and Nash-type
versions of the studied inequalities.
Archive classification: math.FA math.MG
Remarks: 37 pages
Submitted from: emanuel.milman at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.5695
or
http://arXiv.org/abs/1308.5695
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Fernando Albiac and Jose L Ansorena
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 30 Aug 2013 14:53:45 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Optimal average approximations
for functions mapping in quasi-Banach spaces" by Fernando Albiac and
Jose L Ansorena.
Abstract: In 1994, M. M. Popov [On integrability in F-spaces, Studia
Math. no 3, 205-220] showed that the fundamental theorem of calculus
fails, in general, for functions mapping from a compact interval of the
real line into the lp-spaces for 0<p<1, and the question arose whether
such a significant result might hold in some non-Banach spaces. In this
article we completely settle the problem by proving that the fundamental
theorem of calculus breaks down in the context of any non-locally convex
quasi-Banach space. Our approach introduces the tool of Riemann-integral
averages of continuous functions, and uses it to bring out to light
the differences in behavior of their approximates in the lack of local
convexity. As a by-product of our work we solve a problem raised in [F.
Albiac and J.L. Ansorena, Lipschitz maps and primitives for continuous
functions in quasi-Banach space, Nonlinear Anal. 75 (2012), no. 16,
6108-6119] on the different types of spaces of differentiable functions
with values on a quasi-Banach space.
Archive classification: math.FA
Mathematics Subject Classification: 46A16, 46G05
Remarks: 14 pages
Submitted from: joseluis.ansorena at unirioja.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.6127
or
http://arXiv.org/abs/1308.6127
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Hui Zhang and Lizhi Cheng
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 30 Aug 2013 14:55:30 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "New bounds for circulant
Johnson-Lindenstrauss embeddings" by Hui Zhang and Lizhi Cheng.
Abstract: This paper analyzes circulant Johnson-Lindenstrauss (JL)
embeddings which, as an important class of structured random JL
embeddings, are formed by randomizing the column signs of a circulant
matrix generated by a random vector. With the help of recent decoupling
techniques and matrix-valued Bernstein inequalities, we obtain a new
bound $k=O(\epsilon^{-2}\log^{(1+\delta)} (n))$ for Gaussian circulant
JL embeddings. Moreover, by using the Laplace transform technique
(also called Bernstein's trick), we extend the result to subgaussian
case. The bounds in this paper offer a small improvement over the current
best bounds for Gaussian circulant JL embeddings for certain parameter
regimes and are derived using more direct methods.
Archive classification: cs.IT math.FA math.IT
Remarks: 11 pages; accepted by Communications in Mathematical Sciences
Submitted from: h.zhang1984 at 163.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.6339
or
http://arXiv.org/abs/1308.6339
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michael Dymond
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 30 Aug 2013 14:57:06 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Avoiding sigma-porous sets in
Hilbert spaces" by Michael Dymond.
Abstract: We give a constructive proof that any $\sigma$-porous
subset of a Hilbert space has Lebesgue measure zero on typical $C^{1}$
curves. Further, we discover that this result does not extend to all
forms of porosity; we find that even power-$p$ porous sets may meet many
$C^{1}$ curves in positive measure.
Archive classification: math.FA
Submitted from: dymondm at maths.bham.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.6420
or
http://arXiv.org/abs/1308.6420
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Leandro Candido
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 30 Aug 2013 14:58:27 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On embeddings of $C_0(K)$ spaces
into $C_0(J,X)$ spaces" by Leandro Candido.
Abstract: Let $C_0(K, X)$ denote the space of all continuous $X$-valued
functions defined on the locally compact Hausdorff space $K$ which vanish
at infinity, provided with the supremum norm. If $X$ is the scalar field,
we denote $C_0(K, X)$ by simply $C_0(K)$. If $K$ is compact these spaces
will be denoted by $C(K,X)$ and $C(K)$ respectively. In this paper we
study whether some aspects of the space $K$ are determined by $J$ and
the geometry of the Banach space $X$, if there is a linear embeddind of
$C_0(K)$ into $C_0(J,X)$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46E40, Secondary 46B25
Submitted from: lc at ime.usp.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1308.6555
or
http://arXiv.org/abs/1308.6555
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Witold Marciszewski and Grzegorz Plebanek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Sep 2013 15:59:04 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On Borel structures in the Banach
space C(\beta\omega)" by Witold Marciszewski and Grzegorz Plebanek.
Abstract: M. Talagrand showed that, for the Cech-Stone compactification
\beta\omega\ of the space of natural numbers, the norm and the weak
topology generate different Borel structures in the Banach space
C(\beta\omega). We prove that the Borel structures in C(\beta\omega)
generated by the weak and the pointwise topology are also different.
We also show that in C(\omega*), where \omega*=\beta\omega - \omega,
there is no countable family of pointwise Borel sets separating functions
from C(\omega*).
Archive classification: math.FA
Mathematics Subject Classification: 46B26, 46E15, 54C35, 54H05
Remarks: 14 pages
Submitted from: grzes at math.uni.wroc.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.1908
or
http://arXiv.org/abs/1309.1908
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Krzysztof Chris Ciesielski, Jose L.
Gamez-Merino, Daniel Pellegrino, and Juan B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Sep 2013 16:01:13 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lineability, spaceability,
and additivity cardinals for Darboux-like functions" by Krzysztof
Chris Ciesielski, Jose L. Gamez-Merino, Daniel Pellegrino, and Juan
B. Seoane-Sepulveda.
Abstract: We introduce the concept of {\em maximal lineability cardinal
number}, $\mL(M)$, of a subset $M$ of a topological vector space and
study its relation to the cardinal numbers known as: additivity $A(M)$,
homogeneous lineability $\HL(M)$, and lineability $\LL(M)$ of $M$. In
particular, we will describe, in terms of $\LL$, the lineability and
spaceability of the families of the following Darboux-like functions on
$\real^n$, $n\ge 1$: extendable, Jones, and almost continuous functions.
Archive classification: math.FA
Submitted from: jseoane at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.1965
or
http://arXiv.org/abs/1309.1965
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Joaquim Martin and Mario Milman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Sep 2013 16:02:48 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Integral isoperimetric transference
and dimensionless Sobolev inequalities" by Joaquim Martin and Mario
Milman.
Abstract: We introduce the concept of Gaussian integral isoperimetric
transference and show how it can be applied to obtain a new class of
sharp Sobolev-Poincar\'{e} inequalities with constants independent
of the dimension. In the special case of $L^{q}$ spaces on the unit
$n-$dimensional cube our results extend the recent inequalities that
were obtained in \cite{FKS} using extrapolation.
Archive classification: math.FA
Submitted from: mario.milman at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.1980
or
http://arXiv.org/abs/1309.1980
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jin Xi Chen, Zi Li Chen, and Guo Xing Ji
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Sep 2013 16:04:33 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Almost limited sets in Banach
lattices" by Jin Xi Chen, Zi Li Chen, and Guo Xing Ji.
Abstract: We introduce and study the class of almost limited sets in
Banach lattices, that is, sets on which every disjoint weak$^{*}$ null
sequence of functionals converges uniformly to zero. It is established
that a Banach lattice has order continuous norm if and only if almost
limited sets and $L$-weakly compact sets coincide. In particular, in terms
of almost Dunford-Pettis operators into $c_{0}$, we give an operator
characterization of those $\sigma$-Dedekind complete Banach lattices
whose relatively weakly compact sets are almost limited, that is, for a
$\sigma$-Dedekind Banach lattice $E$, every relatively weakly compact
set in $E$ is almost limited if and only if every continuous linear
operator $T:E\rightarrow c_{0}$ is an almost Dunford-Pettis operator.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B42, Secondary 46B50, 47B65
Remarks: 11 pages
Submitted from: jinxichen at home.swjtu.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.2020
or
http://arXiv.org/abs/1309.2020
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Marek Cuth, Martin Rmoutil, and Miroslav
Zeleny
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Sep 2013 16:08:20 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On separable determination of
sigma-P-porous sets in Banach spaces" by Marek Cuth, Martin Rmoutil,
and Miroslav Zeleny.
Abstract: We use a method involving elementary submodels and a partial
converse of Foran lemma to prove separable reduction theorems concerning
Suslin sigma-P-porous sets where "P" can be from a rather wide class
of porosity-like relations in complete metric spaces. In particular, we
separably reduce the notion of Suslin cone small set in Asplund spaces. As
an application we prove a theorem stating that a continuous approximately
convex function on an Asplund space is Frechet differentiable up to a
cone small set.
Archive classification: math.FA
Mathematics Subject Classification: 46B26, 28A05, 54E35, 58C20
Submitted from: cuthm5am at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.2174
or
http://arXiv.org/abs/1309.2174
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Piotr Niemiec
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Sep 2013 16:09:50 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Bounded convergence theorems"
by Piotr Niemiec.
Abstract: There are presented certain results on extending continuous
linear operators defined on spaces of E-valued continuous functions
(defined on a compact Hausdorff space X) to linear operators defined
on spaces of E-valued measurable functions in a way such that uniformly
bounded sequences of functions that converge pointwise in the weak (or
norm) topology of E are sent to sequences that converge in the weak,
norm or weak* topology of the target space. As an application, a new
description of uniform closures of convex subsets of C(X,E) is given. Also
new and strong results on integral representations of continuous linear
operators defined on C(X,E) are presented. A new classes of vector
measures are introduced and various bounded convergence theorems for
them are proved.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46G10, Secondary 46E40
Remarks: 31 pages
Submitted from: piotr.niemiec at uj.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.2612
or
http://arXiv.org/abs/1309.2612
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Cyril Tintarev
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Sep 2013 16:13:05 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Concentration analysis and
cocompactness" by Cyril Tintarev.
Abstract: Loss of compactness that occurs in may significant PDE settings
can be expressed in a well-structured form of profile decomposition for
sequences. Profile decompositions are formulated in relation to a triplet
$(X,Y,D)$, where $X$ and $Y$ are Banach spaces, $X\hookrightarrow Y$, and
$D$ is, typically, a set of surjective isometries on both $X$ and $Y$. A
profile decomposition is a representation of a bounded sequence in $X$
as a sum of elementary concentrations of the form $g_kw$, $g_k\in D$,
$w\in X$, and a remainder that vanishes in $Y$. A necessary requirement
for $Y$ is, therefore, that any sequence in $X$ that develops no
$D$-concentrations has a subsequence convergent in the norm of $Y$. An
imbedding $X\hookrightarrow Y$ with this property is called $D$-cocompact,
a property weaker than, but related to, compactness. We survey known
cocompact imbeddings and their role in profile decompositions.
Archive classification: math.AP math.FA
Submitted from: tintarev at math.uu.se
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.3431
or
http://arXiv.org/abs/1309.3431
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Marek Balcerzak, Adam Majchrzycki, and
Filip Strobin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Sep 2013 16:14:56 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Uniform openness of multiplication
in Banach spaces $L _p$" by Marek Balcerzak, Adam Majchrzycki, and
Filip Strobin.
Abstract: We show that multiplication from $L_p\times L_q$ to $L_1$
(for $p,q\in [1,\infty]$, $1/p+1/q=1$) is a uniformly open mapping. We
also prove the uniform openness of the multiplication from $\ell_1\times
c_0$ to $\ell_1$. This strengthens the former results obtained by
M. Balcerzak, A.~Majchrzycki and A. Wachowicz.
Archive classification: math.FA
Mathematics Subject Classification: 46B25, 47A06, 54C10
Remarks: 8 pages
Submitted from: filip.strobin at p.lodz.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.3433
or
http://arXiv.org/abs/1309.3433
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mukhtar Ibragimov and Karimbergen
Kudaybergenov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Sep 2013 16:16:27 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Geometric description of
L$_1$-Spaces" by Mukhtar Ibragimov and Karimbergen Kudaybergenov.
Abstract: We describe strongly facially symmetric spaces which are
isometrically isomorphic to L$_1$-space.
Archive classification: math.OA
Mathematics Subject Classification: 46B20
Remarks: published in Russian Mathematics, 57, No 5, 2013, 16-21
Submitted from: karim20061 at yandex.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.3620
or
http://arXiv.org/abs/1309.3620
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Luis Bernal-Gonzalez and Manuel
Ordonez-Cabrera
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Sep 2013 16:18:38 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lineability criteria, with
applications" by Luis Bernal-Gonzalez and Manuel Ordonez-Cabrera.
Abstract: Lineability is a property enjoyed by some subsets within
a vector space X. A subset A of X is called lineable whenever A
contains, except for zero, an infinite dimensional vector subspace. If,
additionally, X is endowed with richer structures, then the more
stringent notions of dense-lineability, maximal dense-lineability
and spaceability arise naturally. In this paper, several lineability
criteria are provided and applied to specific topological vector spaces,
mainly function spaces. Sometimes, such criteria furnish unified proofs
of a number of scattered results in the related literature. Families of
strict-order integrable functions, hypercyclic vectors, non-extendable
holomorphic mappings, Riemann non-Lebesgue integrable functions,
sequences not satisfying the Lebesgue dominated convergence theorem,
nowhere analytic functions, bounded variation functions, entire functions
with fast growth and Peano curves, among others, are analyzed from the
point of view of lineability.
Archive classification: math.FA
Mathematics Subject Classification: 15A03, 26A46, 28A25, 30B40, 46E10,
46E30, 47A16
Remarks: 38 pages
Submitted from: lbernal at us.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.3656
or
http://arXiv.org/abs/1309.3656
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gines Lopez Perez and Jose A. Soler Arias
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Sep 2013 12:59:37 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Weak-star point of continuity
property and Schauder bases" by Gines Lopez Perez and Jose A. Soler
Arias.
Abstract: We characterize the weak-star point of continuity property for
subspaces of dual spaces with separable predual and we deduce that the
weak-star point of continuity property is determined by subspaces with
a Schauder basis in the natural setting of dual spaces of separable
Banach spaces. As a consequence of the above characterization we
get that a dual space satisfies the Radon-Nikodym property if, and
only if, every seminormalized topologically weak-star null tree has
a boundedly complete branch, which improves some results in \cite{DF}
obtained for the separable case. Also, as a consequence of the above
characterization, the following result obtained in \cite{R1} is deduced:
{\it every seminormalized basic sequence in a Banach space with the
point of continuity property has a boundedly complete subsequence
Archive classification: math.FA
Submitted from: glopezp at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.3862
or
http://arXiv.org/abs/1309.3862
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Julio Becerra Guerrero, Gines Lopez-Perez,
and Abraham Rueda Zoca
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Sep 2013 13:02:08 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Octahedral norms and convex
combination of slices in Banach spaces" by Julio Becerra Guerrero,
Gines Lopez-Perez, and Abraham Rueda Zoca.
Abstract: We study the relation between octahedral norms, Daugavet
property and the size of convex combinations of slices in Banach
spaces. We prove that the norm of an arbitrary Banach space is octahedral
if, and only if, every convex combination of $w^*$-slices in the dual unit
ball has diameter $2$, which answer an open question. As a consequence
we get that the Banach spaces with the Daugavet property and its dual
spaces have octahedral norms. Also, we show that for every separable
Banach space containing $\ell_1$ and for every $\varepsilon >0$ there
is an equivalent norm so that every convex combination of $w^*$-slices
in the dual unit ball has diameter at least $2-\varepsilon$.
Archive classification: math.FA
Submitted from: glopezp at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.3866
or
http://arXiv.org/abs/1309.3866
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jan-David Hardtke
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Sep 2013 13:03:56 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some remarks on generalised lush
spaces" by Jan-David Hardtke.
Abstract: X. Huang et al. recently introduced the notion of
generalised lush (GL) spaces, which, at least for separable spaces, is
a generalisation of the concept of lushness introduced by K. Boyko et
al. in 2007. The main result of Huang et al. is that every GL-space has
the so called Mazur-Ulam property (MUP). In this note, we will prove some
properties of GL-spaces (further than those already established by Huang
et al.), for example, every $M$-ideal in a GL-space is again a GL-space,
ultraproducts of GL-spaces are again GL-spaces, and if the bidual $X^{**}$
of a Banach space $X$ is GL, then $X$ itself still has the MUP.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 15 pages
Submitted from: hardtke at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.4358
or
http://arXiv.org/abs/1309.4358
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Spiros Argyros, Kevin Beanland and Pavlos
Motakis(Correction)
From: Dale Alspach <alspach at math.okstate.edu>
Date: Mon, 30 Sep 2013 13:19:28 -0500
To: banach at math.okstate.edu, alspach at math.okstate.edu
The URLs were wrong in the previous email.
This is an announcement for the paper "Strictly singular operators in
Tsirelson like spaces" by Spiros Argyros, Kevin Beanland and Pavlos
Motakis.
Abstract: For each $n \in \mathbb{N}$ a Banach space
$\mathfrak{X}_{0,1}^n$ is constructed is having the property that every
normalized weakly null sequence generates either a $c_0$ or $\ell_1$
spreading models and every infinite dimensional subspace has weakly
null sequences generating both $c_0$ and $\ell_1$ spreading models. The
space $\mathfrak{X}_{0,1}^n$ is also quasiminimal and for every infinite
dimensional closed subspace $Y$ of $\mathfrak{X}_{0,1}^n$, for every
$S_1,S_2,\ldots,S_{n+1}$ strictly singular operators on $Y$, the operator
$S_1S_2\cdots S_{n+1}$ is compact. Moreover, for every subspace $Y$
as above, there exist $S_1,S_2,\ldots,S_n$ strictly singular operators
on $Y$, such that the operator $S_1S_2\cdots S_n$ is non-compact.
Archive classification: math.FA
Remarks: 45 pages
Submitted from: kbeanland at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.4516
or
http://arXiv.org/abs/1309.4516
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Simon Lucking
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Sep 2013 13:12:00 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Daugavet property and
translation-invariant subspaces" by Simon Lucking.
Abstract: Let $G$ be an infinite, compact abelian group and
let $\varLambda$ be a subset of its dual group $\varGamma$. We
study the question which spaces of the form $C_\varLambda(G)$ or
$L^1_\varLambda(G)$ and which quotients of the form $C(G)/C_\varLambda(G)$
or $L^1(G)/L^1_\varLambda(G)$ have the Daugavet property. We show that
$C_\varLambda(G)$ is a rich subspace of $C(G)$ if and only if $\varGamma
\setminus \varLambda^{-1}$ is a semi-Riesz set. If $L^1_\varLambda(G)$ is
a rich subspace of $L^1(G)$, then $C_\varLambda(G)$ is a rich subspace of
$C(G)$ as well. Concerning quotients, we prove that $C(G)/C_\varLambda(G)$
has the Daugavet property, if $\varLambda$ is a Rosenthal set, and that
$L^1_\varLambda(G)$ is a poor subspace of $L^1(G)$, if $\varLambda$
is a nicely placed Riesz set.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 43A46
Remarks: 20 pages
Submitted from: simon.luecking at fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.4567
or
http://arXiv.org/abs/1309.4567
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Hana Bendova
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Sep 2013 13:15:39 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Quantitative Grothendieck property"
by Hana Bendova.
Abstract: A Banach space $X$ is Grothendieck if the weak and the weak$^*$
convergence of sequences in the dual space $X^*$ coincide. The space
$\ell^\infty$ is a classical example of a Grothendieck space due to
Grothendieck. We introduce a quantitative version of the Grothendieck
property, we prove a quantitative version of the above-mentioned
Grothendieck's result and we construct a Grothendieck space which is
not quantitatively Grothendieck. We also establish the quantitative
Grothendieck property of $L^\infty(\mu)$ for a $\sigma$-finite measure
$\mu$.
Archive classification: math.FA
Mathematics Subject Classification: 46B26, 46B04, 46A20
Remarks: 9 pages, 0 figures, submitted to the Journal of Mathematical
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.4684
or
http://arXiv.org/abs/1309.4684
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by D.I. Florentin, V.D. Milman, and R.
Schneider
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Sep 2013 14:34:18 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A characterization of the mixed
discriminant" by D.I. Florentin, V.D. Milman, and R. Schneider.
Abstract: We characterize the mixed discriminant of positive semi definite
matrices using its most basic properties. As a corollary we establish
its minimality among non negative and multi additive functionals.
Archive classification: math.FA
Submitted from: danflorentin at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.4798
or
http://arXiv.org/abs/1309.4798
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Julio Becerra Guerrero, Gines Lopez-Perez
and Abraham Rueda Zoca
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Sep 2013 14:36:52 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Extreme differences between weakly
open subsets and convex of slices in Banach spaces" by Julio Becerra
Guerrero, Gines Lopez-Perez and Abraham Rueda Zoca.
Abstract: We show that every Banach space containing isomorphic copies
of $c_0$ can be equivalently renormed so that every nonempty relatively
weakly open subset of its unit ball has diameter 2 and, however, its
unit ball still contains convex combinations of slices with diameter
arbitrarily small, which improves in a optimal way the known results
about the size of this kind of subsets in Banach spaces.
Archive classification: math.FA
Submitted from: glopezp at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.4950
or
http://arXiv.org/abs/1309.4950
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by T. Oikhberg and E. Spinu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Sep 2013 14:39:18 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Operator ideals on non-commutative
function spaces" by T. Oikhberg and E. Spinu.
Abstract: Suppose $X$ and $Y$ are Banach spaces, and ${\mathcal{I}}$,
${\mathcal{J}}$ are operator ideals (for instance, the ideals of strictly
singular, weakly compact, or compact operators). Under what conditions
does the inclusion ${\mathcal{I}}(X,Y) \subset {\mathcal{J}}(X,Y)$,
or the equality ${\mathcal{I}}(X,Y) = {\mathcal{J}}(X,Y)$, hold? We
examine this question when ${\mathcal{I}}, {\mathcal{J}}$ are the
ideals of Dunford-Pettis, strictly (co)singular, finitely strictly
singular, inessential, or (weakly) compact operators, while $X$ and $Y$
are non-commutative function spaces. Since such spaces are ordered,
we also address the same questions for positive parts of such ideals.
Archive classification: math.OA
Submitted from: spinu at ualberta.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.5434
or
http://arXiv.org/abs/1309.5434
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel J. Fresen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Sep 2013 14:40:43 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Euclidean grid structures in
Banach spaces" by Daniel J. Fresen.
Abstract: We study the way in which the Euclidean subspaces of a Banach
space fit together, somewhat in the spirit of the Kashin decomposition.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 52A23, 46B09, 52A21, 46B07
Remarks: 16 pages
Submitted from: daniel.fresen at yale.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.5526
or
http://arXiv.org/abs/1309.5526
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Veronica Dimant and Pablo Sevilla-Peris
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Sep 2013 14:42:37 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Summation of coefficients
of polynomials on $\ell_{p}$ spaces" by Veronica Dimant and Pablo
Sevilla-Peris.
Abstract: We investigate the summability of the coefficients of
$m$-homogeneous polynomials and $m$-linear mappings defined on
$\ell_{p}$-spaces. In our research we obtain results on the summability
of the coefficients of $m$-linear mappings defined on $\ell_{p_{1}} \times
\cdots \times \ell_{p_{m}}$. The first results in this respect go back to
Littlewood and Bohnenblust and Hille (for bilinear and $m$-linear forms
on $c_{0}$) and Hardy and Littlewood and Praciano-Pereira (for bilinear
and $m$-linear forms on arbitrary $\ell_{p}$-spaces). Our results recover
and in some case complete these old results through a general approach
on vector valued $m$-linear mappings.
Archive classification: math.FA
Submitted from: psevilla at mat.upv.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.6063
or
http://arXiv.org/abs/1309.6063
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Benoit Collins, Piotr Gawron, Alexander E.
Litvak, and Karol Zyczkowski
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Sep 2013 14:45:01 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Numerical range for random
matrices" by Benoit Collins, Piotr Gawron, Alexander E. Litvak, and
Karol Zyczkowski.
Abstract: We analyze the numerical range of high-dimensional random
matrices, obtaining limit results and corresponding quantitative estimates
in the non-limit case. We show that the numerical range of complex
Ginibre ensemble converges to the disk of radius $\sqrt{2}$. Since the
spectrum of non-hermitian random matrices from the Ginibre ensemble lives
asymptotically in a neighborhood of the unit disk, it follows that the
outer belt of width $\sqrt{2}-1$ containing no eigenvalues can be seen
as a quantification the non-normality of the complex Ginibre random
matrix. We also show that the numerical range of upper triangular
Gaussian matrices converges to the same disk of radius $\sqrt{2}$,
while all eigenvalues are equal to zero and we prove that the operator
norm of such matrices converges to $\sqrt{2e}$.
Archive classification: math.OA math.FA math.PR quant-ph
Mathematics Subject Classification: 5A60, 47A12, 15B52 (primary), 46B06,
60B20 (secondary)
Remarks: 22 pages, 4 figures
Submitted from: gawron at iitis.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.6203
or
http://arXiv.org/abs/1309.6203
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Vitalii Marchenko
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Sep 2013 14:46:38 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Isomorphic Schauder decompositions
in certain Banach spaces" by Vitalii Marchenko.
Abstract: We extend a theorem of Kato on similarity for sequences
of projections in Hilbert spaces to the case of isomorphic
Schauder decompositions in certain Banach spaces. To this end we use
$\ell_{\Psi}$-Hilbertian and $\infty$-Hilbertian Schauder decompositions
instead of orthogonal Schauder decompositions, generalize the concept of
an orthogonal Schauder decomposition in a Hilbert space and introduce
the class of spaces with Schauder-Orlicz decompositions. Furthermore,
we generalize the notions of type, cotype, infratype and $M$-cotype
of a Banach space and study the properties of unconditional Schauder
decompositions in spaces possessing certain geometric structure.
Archive classification: math.FA
Mathematics Subject Classification: 47A46, 46B15, 47B40
Remarks: 35 pages
Submitted from: vitalii.marchenko at karazin.ua
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.6552
or
http://arXiv.org/abs/1309.6552
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Conference Announcement - First Brazilian Workshop in
Geometry of Banach Spaces: August 2014
From: valentin ferenczi <ferenczi.math at gmail.com>
Date: Mon, 7 Oct 2013 18:11:25 -0300 (16:11 CDT)
To: banach at math.okstate.edu
1st ANNOUNCEMENT OF BWB 2014
First Brazilian Workshop in Geometry of Banach Spaces
August 25-29, 2014
Maresias, São Paulo State, Brazil.
This is the 1st announcement for the First Brazilian Workshop in
Geometry of Banach Spaces, organized by the University of São Paulo
(USP), in the week August 25-29, 2014.
This international conference will take place at the Beach Hotel
Maresias, on the coast of São Paulo State, in Maresias. The scientific
program will focus on the theory of geometry of Banach spaces, with
emphasis on the following directions: linear theory of infinite
dimensional spaces and its relations to Ramsey theory, homological
theory and set theory; nonlinear theory; and operator theory.
The webpage of the Workshop may be found at
http://www.ime.usp.br/~banach/bwb2014/
Registration will start in early 2014. Additional scientific,
practical and financial information will be given at that time.
Plenary speakers:
S. A. Argyros (Nat. Tech. U. Athens)
J. M. F. Castillo (U. Extremadura)
P. Dodos (U. Athens)
G. Godefroy (Paris 6)
R. Haydon (U. Oxford)
W. B. Johnson (Texas A&M)
P. Koszmider (Polish Acad. Warsaw)
G. Pisier (Paris 6 & Texas A&M)
C. Rosendal (U. Illinois Chicago)
G. Schechtman (Weizmann Inst.)
Th. Schlumprecht (Texas A&M)
S. Todorcevic (Paris 7 & U. Toronto)
Scientific committee
J. M. F. Castillo (U. Extremadura)
V. Ferenczi (U. São Paulo)
R. Haydon (U. Oxford)
W. B. Johnson (Texas A&M)
G. Pisier (Paris 6 & Texas A&M)
Th. Schlumprecht (Texas A&M)
S. Todorcevic (Paris 7 & U. Toronto)
We are looking forward to meeting you next year in Brazil,
F. Baudier, C. Brech, V. Ferenczi, E. M. Galego, and J. Lopez-Abad.
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Matthew Tarbard
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Oct 2013 14:50:54 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Operators on Banach spaces of
Bourgain-Delbaen type" by Matthew Tarbard.
Abstract: We begin by giving a detailed exposition of the original
Bourgain-Delbaen construction and the generalised construction due to
Argyros and Haydon. We show how these two constructions are related,
and as a corollary, are able to prove that there exists some $\delta >
0$ and an uncountable set of isometries on the original Bourgain-Delbaen
spaces which are pairwise distance $\delta$ apart.
We subsequently extend these ideas to obtain our main results. We
construct new Banach spaces of Bourgain-Delbaen type, all of which
have $\ell_1$ dual. The first class of spaces are HI and possess few,
but not very few operators. We thus have a negative solution to the
Argyros-Haydon question. We remark that all these spaces have finite
dimensional Calkin algebra, and we investigate the corollaries of this
result. We also construct a space with $\ell_1$ Calkin algebra and show
that whilst this space is still of Bourgain-Delbaen type with $\ell_1$
dual, it behaves somewhat differently to the first class of spaces.
Finally, we briefly consider shift-invariant $\ell_1$ preduals,
and hint at how one might use the Bourgain-Delbaen construction to
produce new, exotic examples.
Archive classification: math.FA
Remarks: Oxford University DPhil Thesis
Submitted from: matthew.tarbard at sjc.ox.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.7469
or
http://arXiv.org/abs/1309.7469
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Felix Cabello Sanchez, Joanna Garbulinska,
and Wieslaw Kubis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Oct 2013 14:53:10 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Quasi-Banach spaces of almost
universal disposition" by Felix Cabello Sanchez, Joanna Garbulinska,
and Wieslaw Kubis.
Abstract: We show that for each $p\in(0,1]$ there exists a separable
$p$-Banach space $\mathbb G_p$ of almost universal disposition, that
is, having the following extension property: for each $\epsilon>0$ and
each isometric embedding $g:X\to Y$, where $Y$ is a finite dimensional
$p$-Banach space and $X$ is a subspace of $\mathbb G_p$, there is an
$\epsilon$-isometry $f:Y\to \mathbb G_p$ such that $x=f(g(x))$ for all
$x\in X$.
Such a space is unique, up to isometries, does contain an isometric copy
of each separable $p$-Banach space and has the remarkable property of
being ``locally injective'' amongst $p$-Banach spaces.
We also present a nonseparable generalization which is of universal
disposition for separable spaces and ``separably injective''. No separably
injective $p$-Banach space was previously known for $p<1$.
Archive classification: math.FA
Mathematics Subject Classification: 46A16, 46B04
Remarks: 22 pages
Submitted from: kubis at math.cas.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1309.7649
or
http://arXiv.org/abs/1309.7649
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mathieu Meyer, Carsten Schuett, and
Elisabeth M. Werner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Oct 2013 14:55:16 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Dual affine invariant points"
by Mathieu Meyer, Carsten Schuett, and Elisabeth M. Werner.
Abstract: An affine invariant point on the class of convex bodies in
R^n, endowed with the Hausdorff metric, is a continuous map p which is
invariant under one-to-one affine transformations A on R^n, that is,
p(A(K))=A(p(K)).
We define here the new notion of dual affine point q of an affine
invariant point p by the formula q(K^{p(K)})=p(K) for every convex body K,
where K^{p(K)} denotes the polar of K with respect to p(K).
We investigate which affine invariant points do have a dual point,
whether this dual point is unique and has itself a dual point. We define
a product on the set of affine invariant points, in relation with duality.
Finally, examples are given which exhibit the rich structure of the
set of affine invariant points.
Archive classification: math.FA
Submitted from: elisabeth.werner at case.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.0128
or
http://arXiv.org/abs/1310.0128
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Olivier Guedon
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Oct 2013 14:57:23 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Concentration phenomena in high
dimensional geometry" by Olivier Guedon.
Abstract: The purpose of this note is to present several aspects of
concentration phenomena in high dimensional geometry. At the heart of
the study is a geometric analysis point of view coming from the theory
of high dimensional convex bodies. The topic has a broad audience going
from algorithmic convex geometry to random matrices. We have tried to
emphasize different problems relating these areas of research. Another
connected area is the study of probability in Banach spaces where some
concentration phenomena are related with good comparisons between the
weak and the strong moments of a random vector.
Archive classification: math.FA
Remarks: This paper is written after a plenary talk given in August
2012 at the "Journ\'ees MAS" organized in Clermont Ferrand. To appear
in ESAIM Proceedings
Submitted from: olivier.guedon at univ-mlv.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.1204
or
http://arXiv.org/abs/1310.1204
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Foivos Xanthos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Oct 2013 14:58:40 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A version of Kalton's theorem
for the space of regular operators" by Foivos Xanthos.
Abstract: In this note we extend some recent results in the space of
regular operators. In particular, we provide the following Banach lattice
version of a classical result of Kalton: Let $E$ be an atomic Banach
lattice with an order continuous norm and $F$ a Banach lattice. Then
the following are equivalent: (i) $L^r(E,F)$ contains no copy of
$\ell_\infty$, \,\, (ii) $L^r(E,F)$ contains no copy of $c_0$, \,\,
(iii) $K^r(E,F)$ contains no copy of $c_0$, \,\, (iv) $K^r(E,F)$ is a
(projection) band in $L^r(E,F)$, \,\, (v) $K^r(E,F)=L^r(E,F)$.
Archive classification: math.FA
Submitted from: foivos at ualberta.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.1591
or
http://arXiv.org/abs/1310.1591
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Claudia Correa and Daniel V. Tausk
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Oct 2013 15:00:06 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Compact lines and the Sobczyk
property" by Claudia Correa and Daniel V. Tausk.
Abstract: We show that Sobczyk's Theorem holds for a new class of
Banach spaces, namely spaces of continuous functions on linearly ordered
compacta.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46E15, 54F05
Remarks: 12 pages
Submitted from: tausk at ime.usp.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.1950
or
http://arXiv.org/abs/1310.1950
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gideon Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Oct 2013 15:01:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "No greedy bases for matrix spaces
with mixed $\ell_p$ and $\ell_q$" by Gideon Schechtman.
Abstract: We show that non of the spaces
$(\bigoplus_{n=1}^\infty\ell_p)_{\ell_q}$, $1\le p\not= q<\infty$, have a
greedy basis. This solves a problem raised by Dilworth, Freeman, Odell and
Schlumprect. Similarly, the spaces $(\bigoplus_{n=1}^\infty\ell_p)_{c_0}$,
$1\le p<\infty$, and $(\bigoplus_{n=1}^\infty c_o)_{\ell_q}$, $1\le
q<\infty$, do not have greedy bases. It follows from that and known
results that a class of Besov spaces on $\R^n$ lack greedy bases as well.
Archive classification: math.FA
Mathematics Subject Classification: 46B15, 41A65, 46B45, 46E35
Submitted from: gideon at weizmann.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.2371
or
http://arXiv.org/abs/1310.2371
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Joanna Garbulinska-Wegrzyn and Wieslaw
Kubis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Oct 2013 15:03:14 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A universal operator on the
Gurarii space" by Joanna Garbulinska-Wegrzyn and Wieslaw Kubis.
Abstract: We construct a nonexpansive linear operator on the Gurarii space
that ``captures" all nonexpansive linear operators between separable
Banach spaces. Some additional properties involving its restrictions
to finite-dimensional subspaces describe this operator uniquely up to
an isometry.
Archive classification: math.FA
Mathematics Subject Classification: 47A05, 47A65, 46B04
Remarks: 17 pages
Submitted from: kubis at math.cas.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.2380
or
http://arXiv.org/abs/1310.2380
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kania and Richard J. Smith
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 13:56:01 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A note on the Bishop property in
compact spaces" by Tomasz Kania and Richard J. Smith.
Abstract: We answer two questions concerning the Bishop property
($\symbishop$), introduced recently by K.P. Hart, T. Kochanek and
the first-named author. There are two versions of ($\symbishop$):
one applies to linear operators and the other to compact Hausdorff
spaces. We show that if $\mathscr{D}$ is a class of compact spaces that
is preserved when taking closed subspaces and Hausdorff quotients, and
which contains no non-metrizable linearly ordered space, then every member
of $\mathscr{D}$ has ($\symbishop$). Examples of such classes include
all $K$ for which $C(K)$ is Lindel\"of in the topology of pointwise
convergence (for instance, all Corson compact spaces) and the class of
Gruenhage compact spaces. We also show that the set of operators on a
$C(K)$-space satisfying ($\symbishop$) does not form a right ideal in
$\mathscr{B}(C(K))$. Some results regarding local connectedness are
also presented.
Archive classification: math.GN math.FA
Submitted from: t.kania at lancaster.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.4035
or
http://arXiv.org/abs/1310.4035
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by M. A. Sofi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 13:57:38 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some problems in functional
analysis inspired by Hahn Banach type theorems" by M. A. Sofi.
Abstract: As a cornerstone of functional analysis, Hahn Banach theorem
constitutes an indispensable tool of modern analysis where its impact
extends beyond the frontiers of linear functional analysis into several
other domains of mathematics, including complex analysis, partial
differential equations and ergodic theory besides many more. The paper is
an attempt to draw attention to certain applications of the Hahn Banach
theorem which are less familiar to the mathematical community, apart from
highlighting certain aspects of the Hahn Banach phenomena which have
spurred intense research activity over the past few years, especially
involving operator analogues and nonlinear variants of this theorem.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 47B10, 46G10
Remarks: 29 pages, 0 figures, accepted in Ann. Func. Anal
Submitted from: aminsofi at kashmiruniversity.ac.in
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.3382
or
http://arXiv.org/abs/1310.3382
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Paul F.X. Muller and Johanna Penteker
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 13:59:38 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "p-summing multiplication operators,
dyadic Hardy Spaces and atomic decomposition" by Paul F.X. Muller and
Johanna Penteker.
Abstract: We constructively determine the Pietsch measure of the
$2$-summing multiplication operator
\[\mathcal{M}_u:\ell^{\infty} \rightarrow H^p, \quad (\varphi_I) \mapsto
\sum \varphi_Ix_Ih_I. \] Our construction of the Pietsch measure for the
multiplication operator $\mathcal{M}_u$ involves the Haar coefficients
of $u$ and its atomic decomposition.
Archive classification: math.FA
Mathematics Subject Classification: 42B30 46B25 46B09 46B42 46E40
47B10 60G42
Remarks: 24 pages
Submitted from: johanna.penteker at jku.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.4312
or
http://arXiv.org/abs/1310.4312
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Niushan Gao
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 14:01:19 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Unbounded order convergence in
dual spaces" by Niushan Gao.
Abstract: A net $(x_\alpha)$ in a vector lattice $X$ is said to be
{unbounded order convergent} (or uo-convergent, for short) to $x\in X$
if the net $(\abs{x_\alpha-x}\wedge y)$ converges to $0$ in order for
all $y\in X_+$. In this paper, we study unbounded order convergence in
dual spaces of Banach lattices. Let $X$ be a Banach lattice. We prove that
every norm bounded uo-convergent net in $X^*$ is $w^*$-convergent iff $X$
has order continuous norm, and that every $w^*$-convergent net in $X^*$
is uo-convergent iff $X$ is atomic with order continuous norm. We also
characterize among $\sigma$-order complete Banach lattices the spaces in
whose dual space every simultaneously uo- and $w^*$-convergent sequence
converges weakly/in norm.
Archive classification: math.FA
Submitted from: niushan at ualberta.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.4438
or
http://arXiv.org/abs/1310.4438
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anna Novikova
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 14:04:06 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lyapunov theorem for q-concave
Banach spaces" by Anna Novikova.
Abstract: Generalization of Lyapunov convexity theorem is proved for
vector measure with values in Banach spaces with unconditional bases,
which are q-concave for some $q<\infty.$
Archive classification: math.FA
Mathematics Subject Classification: 46E30
Remarks: 7 pages
Submitted from: anna.novikova at weizmann.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.4663
or
http://arXiv.org/abs/1310.4663
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Masato Mimura
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 14:05:50 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Sphere equivalence, Banach
expanders, and extrapolation" by Masato Mimura.
Abstract: We study the Banach spectral gap lambda_1(G;X,p) of finite
graphs G for pairs (X,p) of Banach spaces and exponents. We introduce the
notion of sphere equivalence between Banach spaces, and study behavior
of lambda_1(G;X,p) for fixed p in terms of this equivalence. We further
study behavior of lambda_1(G;X,p) for fixed X. As a byproduct, we show
a generalization of Matousek's extrapolation to that for any Banach
space which is sphere equivalent to a uniformly convex Banach space. We
as well prove that expanders are expanders with respects to (X,p) for
any X sphere equivalent to a uniformly curved Banach space and for any
finite p strictly bigger than 1.
Archive classification: math.GR math.CO math.FA math.MG
Remarks: 23 pages, no figure
Submitted from: mimura-mas at m.tohoku.ac.jp
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.4737
or
http://arXiv.org/abs/1310.4737
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Bunyamin Sari and Konstantinos Tyros
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 14:07:34 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the structure of the set of the
higher order spreading models" by Bunyamin Sari and Konstantinos Tyros.
Abstract: We generalize some results concerning the classical notion
of a spreading model for the spreading models of order $\xi$. Among
them, we prove that the set $SM_\xi^w(X)$ of the $\xi$-order spreading
models of a Banach space $X$ generated by subordinated weakly null
$\mathcal{F}$-sequences endowed with the pre-partial order of domination
is a semi-lattice. Moreover, if $SM_\xi^w(X)$ contains an increasing
sequence of length $\omega$ then it contains an increasing sequence of
length $\omega_1$. Finally, if $SM_\xi^w(X)$ is uncountable, then it
contains an antichain of size the continuum.
Archive classification: math.FA
Mathematics Subject Classification: 46B06, 46B25, 46B45
Remarks: 23 pages
Submitted from: chcost at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.5429
or
http://arXiv.org/abs/1310.5429
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Eve Oja
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 14:13:25 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Principle of local reflexivity
respecting subspaces" by Eve Oja.
Abstract: We obtain a strengthening of the principle of local reflexivity
in a general form. The added strength makes local reflexivity operators
respect given subspaces. Applications are given to bounded approximation
properties of pairs, consisting of a Banach space and its subspace.
Archive classification: math.FA
Submitted from: eve.oja at ut.ee
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.6232
or
http://arXiv.org/abs/1310.6232
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. J. Dilworth and B. Randrianantoanina
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 14:14:55 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Almost transitive and maximal
norms in Banach spaces" by S. J. Dilworth and B. Randrianantoanina.
Abstract: We prove that the spaces $\ell_p$, $1<p<\infty, p\ne 2$, and
all infinite-dimensional subspaces of their quotient spaces do not admit
equivalent almost transitive renormings. This answers a problem posed by
Deville, Godefroy and Zizler in 1993. We obtain this as a consequence
of a new property of almost transitive spaces with a Schauder basis,
namely we prove that in such spaces the unit vector basis of $\ell_2^2$
belongs to the two-dimensional asymptotic structure and we obtain some
information about the asymptotic structure in higher dimensions. We also
obtain several other results about properties of classical, Tsirelson
type and non-commutative Banach spaces with almost transitive norms.
Further, we prove that the spaces $\ell_p$, $1<p<\infty$, $p\ne
2$, have continuum different renormings with 1-unconditional bases each
with a different maximal isometry group, and that every symmetric space
other than $\ell_2$ has at least a countable number of such renormings. On
the other hand we show that the spaces $\ell_p$, $1<p<\infty$, $p\ne 2$,
have continuum different renormings each with an isometry group which is
not contained in any maximal bounded subgroup of the group of isomorphisms
of $\ell_p$. This answers a question of Wood.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 46B03, 22F50
Submitted from: randrib at miamioh.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.7139
or
http://arXiv.org/abs/1310.7139
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by M A Sofi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 14:16:16 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Around finite-dimensionality in
functional analysis" by M A Sofi.
Abstract: As objects of study in functional analysis, Hilbert spaces
stand out as special objects of study as do nuclear spaces in view
of a rich geometrical structure they possess as Banach and Frechet
spaces, respectively. On the other hand, there is the class of Banach
spaces including certain function spaces and sequence spaces which
are distinguished by a poor geometrical structure and are subsumed
under the class of so-called Hilbert-Schmidt spaces. It turns out that
these three classes of spaces are mutually disjoint in the sense that
they intersect precisely in finite dimensional spaces. However, it is
remarkable that despite this mutually exclusive character, there is
an underlying commonality of approach to these disparate classes of
objects in that they crop up in certain situations involving a single
phenomenon-the phenomenon of finite dimensionality-which, by definition,
is a generic term for those properties of Banach spaces which hold good
in finite dimensional spaces but fail in infinite dimension.
Archive classification: math.FA
Mathematics Subject Classification: 46A11, 46C15
Citation: RACSAM 2013
Remarks: 22 pages
Submitted from: aminsofi at kashmiruniversity.ac.in
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.7165
or
http://arXiv.org/abs/1310.7165
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Andrei Dorogovtsev and Mikhail Popov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 14:17:53 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Basis entropy in Banach spaces"
by Andrei Dorogovtsev and Mikhail Popov.
Abstract: We introduce and study two notions of entropy in a Banach
space X with a normalized Schauder basis . The geometric entropy E(A)
of a subset A of X is defined to be the infimum of radii of compact
bricks containing A. We obtain several compactness characterizations for
bricks (Theorem 3.7) useful for main results. We also obtain sufficient
conditions on a set in a Hilbert space to have finite unconditional
entropy. For Banach spaces without a Schauder basis we offer another
entropy, called the Auerbach entropy. Finally, we pose some open problems.
Archive classification: math.FA
Mathematics Subject Classification: 46B50, 46B15, 60H07
Remarks: 22 pages
Submitted from: adoro at imath.kiev.ua
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.7248
or
http://arXiv.org/abs/1310.7248
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Denny H. Leung and Lei Li
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 14:19:21 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Order isomorphisms on function
spaces" by Denny H. Leung and Lei Li.
Abstract: The classical theorems of Banach and Stone, Gelfand and
Kolmogorov, and Kaplansky show that a compact Hausdorff space $X$ is
uniquely determined by the linear isometric structure, the algebraic
structure, and the lattice structure, respectively, of the space
$C(X)$. In this paper, it is shown that for rather general subspaces
$A(X)$ and $A(Y)$ of $C(X)$ and $C(Y)$ respectively, any linear bijection
$T: A(X) \to A(Y)$ such that $f \geq 0$ if and only if $Tf \geq 0$ gives
rise to a homeomorphism $h: X \to Y$ with which $T$ can be represented as
a weighted composition operator. The three classical results mentioned
above can be derived as corollaries. Generalizations to noncompact
spaces and other function spaces such as spaces of uniformly continuous
functions, Lipschitz functions and differentiable functions are presented.
Archive classification: math.FA
Mathematics Subject Classification: 46E15
Submitted from: matlhh at nus.edu.sg
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.7351
or
http://arXiv.org/abs/1310.7351
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Denny H. Leung
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 14:20:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Ideals of operators on $(\oplus
\ell^\infty(n))_{\ell^1}$" by Denny H. Leung.
Abstract: The unique maximal ideal in the Banach algebra $L(E)$, $E =
(\oplus \ell^\infty(n))_{\ell^1}$, is identified. The proof relies on
techniques developed by Laustsen, Loy and Read and a dichotomy result
for operators mapping into $L^1$ due to Laustsen, Odell, Schlumprecht
and Zs\'{a}k.
Archive classification: math.FA
Mathematics Subject Classification: 46L10, 46H10
Submitted from: matlhh at nus.edu.sg
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.7352
or
http://arXiv.org/abs/1310.7352
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mubariz Garayev
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 14:22:27 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Solution of invariant subspace
problem in the Hilbert space" by Mubariz Garayev.
Abstract: By applying methods of Duhamel algebra and reproducing kernels,
we prove that every linear bounded operator on the Hardy-Hilbert space
H^{2}(D) has a nontrivial invariant subspace. This solves affirmatively
the Invariant Subspace Problem in the Hilbert space.
Archive classification: math.FA
Mathematics Subject Classification: 47A12
Submitted from: mgarayev at ksu.edu.sa
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.8055
or
http://arXiv.org/abs/1310.8055
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alexander Koldobsky
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 31 Oct 2013 14:24:59 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Slicing inequalities for subspaces
of $L_p.$" by Alexander Koldobsky.
Abstract: We show that the hyperplane conjecture holds for the classes
of $k$-intersection bodies with arbitrary measures in place of volume.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 52A20
Submitted from: koldobskiya at missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1310.8102
or
http://arXiv.org/abs/1310.8102
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Bernhard Hermann Haak and Markus Haase
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Nov 2013 12:57:29 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Square Function Estimates and
Functional Calculi" by Bernhard Hermann Haak and Markus Haase.
Abstract: In this paper the notion of an abstract square function
(estimate) is introduced as an operator X to gamma (H; Y ), where X,
Y are Banach spaces, H is a Hilbert space, and gamma(H; Y ) is the space
of gamma-radonifying operators. By the seminal work of Kalton and Weis,
this definition is a coherent generalisation of the classical notion of
square function appearing in the theory of singular integrals. Given
an abstract functional calculus (E, F , Phi) on a Banach space X,
where F (O) is an algebra of scalar-valued functions on a set O, we
define a square function Phi_gamma(f ) for certain H-valued functions
f on O. The assignment f to Phi_gamma(f ) then becomes a vectorial
functional calculus, and a "square function estimate" for f simply means
the boundedness of Phi_gamma(f ). In this view, all results linking
square function estimates with the boundedness of a certain (usually
the H-infinity) functional calculus simply assert that certain square
function estimates imply other square function estimates. In the present
paper several results of this type are proved in an abstract setting,
based on the principles of subordination, integral representation, and
a new boundedness concept for subsets of Hilbert spaces, the so-called
ell-1 -frame-boundedness. These abstract results are then applied to the
H-infinity calculus for sectorial and strip type operators. For example,
it is proved that any strip type operator with bounded scalar H-infinity
calculus on a strip over a Banach space with finite cotype has a bounded
vectorial H-infinity calculus on every larger strip.
Archive classification: math.FA
Remarks: 49p.
Submitted from: bernhard.haak at math.u-bordeaux1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.0453
or
http://arXiv.org/abs/1311.0453
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Victor Bible
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Nov 2013 12:59:08 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Using boundaries to find smooth
norms" by Victor Bible.
Abstract: The aim of this paper is to present a tool used to find Banach
spaces which have a C^{\infty} smooth equivalent norm. The hypothesis
uses particular countable decompositions of certain subsets of B_{X^*},
namely boundaries. Of interest is that the main result unifies two quite
well known results. In the final section, some new Corollaries are given.
Archive classification: math.FA
Mathematics Subject Classification: 46B03
Remarks: 11 pages
Submitted from: victor.bible at ucdconnect.ie
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.1408
or
http://arXiv.org/abs/1311.1408
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by O.I. Reinov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Nov 2013 13:01:11 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On linear operators with
${\ssize\bold s}$-nuclear adjoints: $0<{\ssize s}\le 1$" by
O.I. Reinov.
Abstract: If $ s\in (0,1]$ and $ T$ is a linear operator with $
s$-nuclear adjoint from a Banach space $ X$ to a Banach space $ Y$ and
if one of the spaces $ X^*$ or $ Y^{***}$ has the approximation property
of order $s,$ \, $AP_s,$ then the operator $ T$ is nuclear. The result
is in a sense exact. For example, it is shown that for each $r\in (2/3,
1]$ there exist a Banach space $Z_0$ and a non-nuclear operator $ T:
Z_0^{**}\to Z_0$ so that $ Z_0^{**}$ has a Schauder basis, $ Z_0^{***}$
has the $AP_s$ for every $s\in (0,r)$ and $T^*$ is $r$-nuclear.
Archive classification: math.FA
Remarks: 11 pages, AMS TeX
Submitted from: orein51 at mail.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.2270
or
http://arXiv.org/abs/1311.2270
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Rainis Haller, Johann Langemets and Mart
Poldvere
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Nov 2013 13:02:53 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On duality of diameter 2
properties" by Rainis Haller, Johann Langemets and Mart Poldvere.
Abstract: It is known that a Banach space has the strong diameter 2
property (i.e. every convex combination of slices of the unit ball has
diameter 2) if and only if the norm on its dual space is octahedral (a
notion introduced by Godefroy and Maurey). We introduce two more versions
of octahedrality, which turn out to be dual properties to the diameter
2 property and its local version (i.e., respectively, every relatively
weakly open subset and every slice of the unit ball has diameter 2). We
study stability properties of different types of octahedrality, which,
by duality, provide easier proofs of many known results on diameter
2 properties.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B22
Submitted from: johann.langemets at ut.ee
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.2177
or
http://arXiv.org/abs/1311.2177
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A. G. Aksoy and J. M. Almira
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Nov 2013 13:08:23 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On approximation schemes and
compactness" by A. G. Aksoy and J. M. Almira.
Abstract: We present an overview of some results about characterization
of compactness in which the concept of approximation scheme has had a
role. In particular, we present several results that were proved by the
second author, jointly with Luther, a decade ago, when these authors
were working on a very general theory of approximation spaces. We then
introduce and show the basic properties of a new concept of compactness,
which was studied by the first author in the eighties, by using a
generalized concept of approximation scheme and its associated Kolmogorov
numbers, which generalizes the classical concept of compactness.
Archive classification: math.FA
Remarks: 18 pages, submitted
Submitted from: jmalmira at ujaen.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.2385
or
http://arXiv.org/abs/1311.2385
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jean Bourgain and Jelani Nelson
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Nov 2013 13:13:04 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Toward a unified theory of sparse
dimensionality reduction in Euclidean space" by Jean Bourgain and Jelani
Nelson.
Abstract: Let $\Phi\in\mathbb{R}^{m\times n}$ be a sparse
Johnson-Lindenstrauss transform [Kane, Nelson, SODA 2012] with
$s$ non-zeroes per column. For $T$ a subset of the unit sphere,
$\varepsilon\in(0,1/2)$ given, we study settings for $m,s$ required to
ensure $$ \mathop{\mathbb{E}}_\Phi \sup_{x\in T} \left|\|\Phi x\|_2^2 - 1
\right| < \varepsilon , $$ i.e. so that $\Phi$ preserves the norm of every
$x\in T$ simultaneously and multiplicatively up to $1+\varepsilon$. In
particular, our most general theorem shows that it suffices to set $m =
\tilde{\Omega}(\gamma_2^2(T) + 1)$ and $s = \tilde{\Omega}(1)$ as long as
$s,m$ additionally satisfy a certain tradeoff condition that is governed
by the geometry of $T$ (and as we show for several examples of interest,
is easy to verify). Here $\gamma_2$ is Talagrand's functional, and we
write $f = \tilde{\Omega}(g)$ to mean $f \ge Cg (\varepsilon^{-1}\log
n)^c$ for some constants $C,c>0$.
Our result can be seen as an extension to sparse $\Phi$ of works of
[Klartag, Mendelson, J. Funct. Anal. 2005], [Gordon, GAFA 1988],
and [Mendelson, Pajor, Tomczak-Jaegermann, GAFA 2007], which were
concerned with dense $\Phi$ having i.i.d. (sub)gaussian entries. Our
work introduces a theory that qualitatively unifies several results
related to the Johnson-Lindenstrauss lemma, subspace embeddings, and
Fourier-based methods for obtaining matrices satisfying the restricted
isometry property.
Archive classification: cs.DS cs.CG cs.IT math.FA math.IT math.PR
Submitted from: minilek at seas.harvard.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.2542
or
http://arXiv.org/abs/1311.2542
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jin Xi Chen, Zi Li Chen, and Guo Xing Ji
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Nov 2013 13:14:36 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Domination by positive weak*
Dunford-Pettis operators on Banach" by Jin Xi Chen, Zi Li Chen, and Guo
Xing Ji.
Abstract: Recently, J. H'michane et al. introduced the class of weak*
Dunford-Pettis operators on Banach spaces, that is, operators which send
weakly compact sets onto limited sets. In this paper the domination
problem for weak* Dunford-Pettis operators is considered. Let $S,
T:E\rightarrow F$ be two positive operators between Banach lattices $E$
and $F$ such that $0\leq S\leq T$. We show that if $T$ is a weak$^{*}$
Dunford-Pettis operator and $F$ is $\sigma$-Dedekind complete, then $S$
itself is weak* Dunford-Pettis.
Archive classification: math.FA math.OA
Mathematics Subject Classification: Primary 46B42, Secondary 46B50, 47B65
Remarks: 8 pages
Submitted from: jinxichen at home.swjtu.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.2808
or
http://arXiv.org/abs/1311.2808
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Nacib Albuquerque, Frederic Bayart, Daniel
Pellegrino, and Seoane Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Nov 2013 13:16:44 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Optimal Hardy-Littlewood type
inequalities for polynomials and multilinear operators" by Nacib
Albuquerque, Frederic Bayart, Daniel Pellegrino, and Seoane Sepulveda.
Abstract: In this paper we obtain quite general forms for Hardy-Littlewood
type inequalities. Moreover, when restricted to the original particular
cases, our approach provides much simple and straightforward proofs. The
technique used is a very recent interpolative approach; this method is
also used in this paper to obtain better constants for vector-valued
Bohnenblust-Hille type inequalities.
Archive classification: math.FA
Remarks: 7 pages
Submitted from: jseoane at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.3177
or
http://arXiv.org/abs/1311.3177
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Dario Cordero-Erausquin, Matthieu
Fradelizi, Grigoris Paouris, and Peter Pivovarov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Nov 2013 13:18:55 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Volume of the polar of random
sets and shadow systems" by Dario Cordero-Erausquin, Matthieu Fradelizi,
Grigoris Paouris, and Peter Pivovarov.
Abstract: We obtain optimal inequalities for the volume of the polar of
random sets, generated for instance by the convex hull of independent
random vectors in Euclidean space. Extremizers are given by random vectors
uniformly distributed in Euclidean balls. This provides a random extension
of the Blaschke-Santalo inequality which, in turn, can be derived by the
law of large numbers. The method involves generalized shadow systems,
their connection to Busemann type inequalities, and how they interact
with functional rearrangement inequalities.
Archive classification: math.FA
Submitted from: pivovarovp at missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.3690
or
http://arXiv.org/abs/1311.3690
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Normuxammad Yadgorov, Mukhtar Ibragimov,
and Karimbergen Kudaybergenov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Nov 2013 13:20:38 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Geometric characterization of
$L_1$-spaces" by Normuxammad Yadgorov, Mukhtar Ibragimov, and Karimbergen
Kudaybergenov.
Abstract: The paper is devoted to a description of all strongly facially
symmetric spaces which are isometrically isomorphic to $L_1$-spaces. We
prove that if $Z$ is a real neutral strongly facially symmetric space
such that every maximal geometric tripotent from the dual space of
$Z$ is unitary then, the space $Z$ is isometrically isomorphic to the
space $L_1(\Omega, \Sigma, \mu),$ where $(\Omega, \Sigma, \mu)$ is an
appropriate measure space having the direct sum property.
Archive classification: math.OA
Mathematics Subject Classification: 46B20
Remarks: Accepted to publication in the journal Studia Mathematica
Submitted from: karim20061 at yandex.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.4429
or
http://arXiv.org/abs/1311.4429
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonin Prochazka and Luis Sanchez-Gonzalez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Nov 2013 14:06:40 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Low distortion embeddings into
Asplund Banach spaces" by Antonin Prochazka and Luis Sanchez-Gonzalez.
Abstract: We give a simple example of a countable metric space that
does not embed bi-Lipschitz with distortion strictly less than 2 into
any Asplund space.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B85
Remarks: 3 pages
Submitted from: antonin.prochazka at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.4584
or
http://arXiv.org/abs/1311.4584
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Pellegrino, Pilar Rueda, and Enrique
A. Sanchez-Perez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Nov 2013 14:08:07 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Weak compactness and strongly
summing multilinear operators" by Daniel Pellegrino, Pilar Rueda, and
Enrique A. Sanchez-Perez.
Abstract: Every absolutely summing linear operator is weakly
compact. However, for strongly summing multilinear operators and
polynomials { one of the most natural extensions of the linear
case to the non linear framework { weak compactness does not hold
in general. We show that a subclass of the class of strongly summing
multilinear operators/polynomials, sharing its main properties such as
Grothendieck's Theorem, Pietsch Domination Theorem and Dvoretzky{Rogers
Theorem, has even better properties like weak compactness and a natural
factorization theorem.
Archive classification: math.FA
Mathematics Subject Classification: 46A32
Submitted from: pilar.rueda at uv.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.4685
or
http://arXiv.org/abs/1311.4685
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Christos Saroglou
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Nov 2013 14:09:12 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Remarks on the conjectured
log-Brunn-Minkowski inequality" by Christos Saroglou.
Abstract: \footnotesize B\"{o}r\"{o}czky, Lutwak, Yang and Zhang recently
conjectured a certain strengthening of the Brunn-Minkowski inequality for
symmetric convex bodies, the so-called log-Brunn-Minkowski inequality. We
establish this inequality together with its equality cases for pairs
of unconditional convex bodies with respect to the same orthonormal
basis. Applications of this fact are discussed. Moreover, we prove that
the log-Brunn-Minkowski inequality is equivalent to the (B)-Theorem for
the uniform measure of the cube (this has been proven by Cordero-Erasquin,
Fradelizi and Maurey for the gaussian measure instead).
Archive classification: math.FA
Remarks: Submitted 30 April,2013
Submitted from: saroglou at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.4954
or
http://arXiv.org/abs/1311.4954
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Christos Saroglou
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Nov 2013 14:10:23 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the equivalence between two
problems of asymmetry on convex bodies" by Christos Saroglou.
Abstract: The simplex was conjectured to be the extremal convex body for
the two following ``problems of asymmetry'':\\ P1) What is the minimal
possible value of the quantity $\max_{K'} |K'|/|K|$? Here, $K'$ ranges
over all symmetric convex bodies contained in $K$.\\ P2) What is the
maximal possible volume of the Blaschke-body of a convex body of volume
1?\\ Our main result states that (P1) and (P2) admit precisely the same
solutions. This complements a result from [{\rm K. B\"{o}r\"{o}czky,
I. B\'{a}r\'{a}ny, E. Makai Jr. and J. Pach}, Maximal volume enclosed by
plates and proof of the chessboard conjecture], Discrete Math. {\bf 69}
(1986), 101--120], stating that if the simplex solves (P1) then the
simplex solves (P2) as well.
Archive classification: math.FA
Remarks: Submitted for publication, November 2013
Submitted from: saroglou at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.4955
or
http://arXiv.org/abs/1311.4955
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] meeting
From: "Gonzalez Ortiz, Manuel" <manuel.gonzalez at unican.es>
Date: Tue, 3 Dec 2013 15:38:30 +0000
To: "banach at www.math.okstate.edu" <banach at math.okstate.edu>
This is an announcement of the Meeting
INTERPOLATION AND BANACH SPACE CONSTRUCTIONS
Castro Urdiales, Cantabria, Spain
2nd–6th June 2014
This Meeting is focused on the topics of interpolation theory,
Banach space constructions and the interplay between them,
and is aimed at researchers in Banach space theory.
It will consist of invited talks, short communications and
discussion time.
Those wishing to deliver a short talk or take part in the poster session
should indicate so when filling the registration form.
Invited speakers include Pandelis Dodos (University of Athens),
Valentin Ferenczi (Universidade de São Paulo), Piotr Koszmider
(Polish Academy of Sciences/Technical University of Łódź),
Jordi López Abad (Instituto de Ciencias Matemáticas) and
Richard Rochberg (Washington University in St. Louis).
For additional information and registration we refer to the web page
of the meeting:
http://www.ciem.unican.es/encuentros/banach/2014/
_______________________________________________
Banach mailing list
Banach at www.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] 2 post-doc positions in Besancon
From: Gilles Lancien <gilles.lancien at univ-fcomte.fr>
Date: Wed, 11 Dec 2013 14:29:10 +0100
To: banach at math.okstate.edu
Dear colleagues,
The ``Laboratoire de Mathématiques de Besançon'' will open two one-year
postdoctoral positions in Functional Analysis, without teaching.
Please find below two separate announcements.
Sincerely yours, Gilles Lancien
-------------------------------------------------------------------------------------------
Postdoctoral position in Functional Analysis.
Duration: One year.
Beginning of contract: September/October 2014.
Job description: we are looking for a postdoctoral fellow who will work
in one of the areas of research developed in the functional analysis
team: operator spaces, operator algebras, noncommutative L_p spaces,
quantum probability and noncommutative harmonic analysis, Banach spaces,
nonlinear geometric functional analysis, functional calculus and
semigroups.
More information on our team is available here:
http://lmb.univ-fcomte.fr/rubrique.php3?id_rubrique=7
The postdoctoral fellow will participate in the activities of our
special trimester ``Geometric and noncommutative methods in functional
analysis'' (September-December 2014). For more information on this
trimester:
http://trimestres-lmb.univ-fcomte.fr/fa
The deadline for the applications is April 10th 2014. We are looking for
applicants who received their Ph.D. recently (or will receive it until
September
2014). The applications should include: a CV, a summary of your research
work and a research project.
Send your application by email to the following address:
af2014 at univ-fcomte.fr
Indicate "PostdocAF2014" in the Subject of your message.
Please write to the same address for more information.
-------------------------------------------------------------------------------------------------
Postdoctoral position in Functional Analysis.
Duration: One year.
Beginning of contract: September/October 2014.
Job description: we are looking for a postdoctoral fellow who will work in
one of the areas of the ANR project OSQPI (Interactions between Operator
Space Theory and Quantum Probability with Applications to Quantum
Information): operator spaces, noncommutative L_p spaces, noncommutative
harmonic analysis, quantum probability, and their applications in quantum
information). Part of the program could also be carried out at partner
institutions in Paris, Lyon, or Toulouse.
The postdoctoral fellow will participate in the activities of our
special trimester ``Geometric and noncommutative methods in functional
analysis'' (September-December 2014). For more information on this
trimester:
http://trimestres-lmb.univ-fcomte.fr/fa
The deadline for the applications is April 10th 2014. We are looking for
applicants who received their Ph.D. recently (or will receive it until
September
2014). The applications should include: a CV, a summary of your research
work and a research project.
Send your application by email to the following address:
af2014 at univ-fcomte.fr
Indicate "PostdocANR" in the Subject of your message.
Please write to the same address for more information.
_______________________________________________
Banach mailing list
Banach at www.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Conference announcement: Stochastic processes and high
dimensional probability distributions.
From: Elizabeth Meckes <ese3 at case.edu>
Date: Mon, 16 Dec 2013 12:57:47 +0100
To: banach at math.okstate.edu
Stochastic processes and high dimensional probability distributionsJune 16
- 20, 2014Euler International Mathematical Institute, Saint-Petersburg,
Russia
A conference in honor of the lifelong contributions of Vladimir
Nikolayevich Sudakov.
The conference will focus on several closely related directions in
Probability Theory and Analysis including: Geometric problems about
Gaussian and other linear stochastic processes; Typical distributions,
measure concentration and high dimensional phenomena; Optimal
transportation and associated Sobolev-type and information-theoretic
inequalities.
Invited speakers are:
V.Bogachev (Moscow University), A.Dembo (Stanford), R.Dudley (MIT),
W.Gangbo
(Georgia Tech), N.Gozlan (Paris-Est), I.Ibragimov (Steklov Institute),
S.Kwapien (Warsaw), R Latala (Warsaw), M.Ledoux (Toulouse), R.McCann
(Toronto),
M.Milman (Florida), V.Milman (Tel Aviv), H. von Weizs\"acker
(Kaiserslautern).
There will be an opportunity for contributed talks.
A preliminary web page for the conference can be found at
http://www.pdmi.ras.ru/EIMI/2014/Sppd/index.html
We are applying for NSF support for travel for US participants; priority
will be given to young researchers (especially students and post-docs)
without other sources of support.
--
Elizabeth S. Meckes
Associate Professor of Mathematics
Case Western Reserve University
_______________________________________________
Banach mailing list
Banach at www.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] School and conference announcement: Besancon, Autumn 2014
From: glancien at math.cnrs.fr
Date: Mon, 16 Dec 2013 21:38:48 +0100
To: banach at math.okstate.edu
Dear colleagues,
As part of the trimester on "Geometric and noncommutative methods in
functional analysis" organized by the "Laboratoire de Mathematiques de
Besancon" during the Autumn 2014, we wish to announce the two
following events.
1) The Autum school on "Nonlinear geometry of Banach spaces and
applications", in Metabief (October 20-24, 2014). The following
mathematicians have kindly accepted our invitation to deliver a short
course: Gilles Godefroy (Université Paris 6), Petr Hajek (Czech
Academy of Sciences and Czech Technical University), Manor Mendel
(Open University of Israel - to be confirmed), Nirina Lovasoa
Randrianarivony (Saint Louis University - to be confirmed), Guoliang
Yu (Texas A&M University).
2) The conference on "Geometric functional analysis and its
applications" in Besancon (October 27-31, 2014). The following main
speakers have already agreed to deliver a plenary lecture: Fernando
Albiac (Univ. Publica de Navarra), Florent Baudier (Texas A&M
University, Paris 6) , Robert Deville (Univ. Bordeaux) , Stephen
Dilworth (Univ. South Carolina), Valentin Ferenczi (Univ. Sao Paulo) ,
Bill Johnson (Texas A&M University), Beata Randrianantoanina (Miami
Univ Ohio), Gideon Schechtman (Weizmann Institute), Thomas
Schlumprecht (Texas A&M University), Alain Valette (Univ. Neuchatel).
Other participants will have the opportunity to give a short talk.
The purpose of these meetings is to bring together researchers and
students with common interest in the field. They will offer many
possibilities for informal discussions. Graduate students and others
beginning their mathematical career are encouraged to participate.
You can visit the following websites:
trimester: http://trimestres-lmb.univ-fcomte.fr/af.html
School in Metabief:
https://trimestres-lmb.univ-fcomte.fr/Autumn-School-on-Nonlinear.html?lang=en
Conference in Besancon:
https://trimestres-lmb.univ-fcomte.fr/Conference-on-Geometric-Functional.html?lang=en
Registration for both events is now open.
The organizers, Gilles Lancien and Tony Prochazka
----- Fin du message transféré -----
_______________________________________________
Banach mailing list
Banach at www.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Amir Livne Bar-on
Date: Tue, 17 Dec 2013 11:13:47 CST
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
This is an announcement for the paper "The (B) conjecture for uniform
measures in the plane" by Amir Livne Bar-on.
Abstract: We prove that for any two centrally-symmetric convex shapes
$K,L \subset \mathbb{R}^2$, the function $t \mapsto |e^t K \cap L|$
is log-concave. This extends a result of Cordero-Erausquin, Fradelizi
and Maurey in the two dimensional case. Possible relaxations of the
condition of symmetry are discussed.
Archive classification: math.FA
Remarks: 10 pages
Submitted from: livnebaron at mail.tau.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.6584
or
http://arXiv.org/abs/1311.6584
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Manaf Adnan Salah
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 17 Dec 2013 11:16:15 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lipschitz
$\left(\mathfrak{m}^L\left(s;q\right),p\right)$ and
$\left(p,\mathfrak{m}^L\left(s;q\right)\right)-$summing maps" by Manaf
Adnan Salah.
Abstract: Building upon the linear version of mixed summable sequences
in arbitrary Banach spaces of A. Pietsch, we introduce a nonlinear
version of his concept and study its properties. Extending previous
work of J. D. Farmer, W. B. Johnson and J. A. Ch\'avez-Dom\'inguez,
we define Lipschitz $\left(\mathfrak{m}^L\left(s;q\right),p\right)$
and Lipschitz $\left(p,\mathfrak{m}^L\left(s;q\right)\right)-$summing
maps and establish inclusion theorems, composition theorems and
several characterizations. Furthermore, we prove that the classes of
Lipschitz $\left(r,\mathfrak{m}^L\left(r;r\right)\right)-$summing maps
with $0<r<1$ coincide. We obtain that every Lipschitz map is Lipschitz
$\left(p,\mathfrak{m}^L\left(s;q\right)\right)-$summing map with $1\leq s<
p$ and $0<q\leq s$ and discuss a sufficient condition for a Lipschitz
composition formula as in the linear case of A. Pietsch. Moreover,
we discuss a counterexample of the nonlinear composition formula, thus
solving a problem by J. D. Farmer and W. B. Johnson.
Archive classification: math.FA
Mathematics Subject Classification: 47L20 47B10
Submitted from: manaf-adnan.salah at uni-jena.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1311.7575
or
http://arXiv.org/abs/1311.7575
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michael Kelly
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 17 Dec 2013 11:18:10 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Blaschke-Santalo Inequality"
by Michael Kelly.
Abstract: The Blaschke-Santalo inequality is the assertion that the volume
product of a symmetric convex body in Euclidean space is maximized by
the Euclidean unit ball. In this paper we give a Fourier analytic proof
of this fact.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 52A40 (Primary), 42A05, 42A85, 52A39,
46E22 (Secondary)
Remarks: 11 pages, 4 figures
Submitted from: mkelly at math.utexas.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.0244
or
http://arXiv.org/abs/1312.0244
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Carando, Daniel Galicer and Damian
Pinasco
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 17 Dec 2013 11:20:36 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Energy integrals and metric
embedding theory" by Daniel Carando, Daniel Galicer and Damian Pinasco.
Abstract: For some centrally symmetric convex bodies $K\subset \mathbb
R^n$, we study the energy integral $$ \sup \int_{K} \int_{K} \|x -
y\|_r^{p}\, d\mu(x) d\mu(y), $$ where the supremum runs over all finite
signed Borel measures $\mu$ on $K$ of total mass one. In the case where
$K = B_q^n$, the unit ball of $\ell_q^n$ (for $1 \leq q \leq 2$) or an
ellipsoid, we obtain the exact value or the correct asymptotical behavior
of the supremum of these integrals.
We apply these results to a classical embedding problem in metric
geometry. We consider in $\mathbb R^n$ the Euclidean distance $d_2$. For
$0 < \alpha < 1$, we estimate the minimum $R$ for which the snowflaked
metric space $(K, d_2^{\alpha})$ may be isometrically embedded on the
surface of a Hilbert sphere of radius $R$.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 51M16, 52A23, 31C45, 51K05, 54E40
Remarks: 18 pages
Submitted from: dgalicer at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.0678
or
http://arXiv.org/abs/1312.0678
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Oleg Reinov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 17 Dec 2013 11:22:24 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On operators with bounded
approximation property" by Oleg Reinov.
Abstract: It is known that any separable Banach space with BAP is a
complemented subspace of a Banach space with a basis. We show that every
operator with bounded approximation property, acting from a separable
Banach space, can be factored through a Banach space with a basis.
Archive classification: math.FA
Mathematics Subject Classification: 46B28
Remarks: 5 pages
Submitted from: orein51 at mail.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.2116
or
http://arXiv.org/abs/1312.2116
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by N. Machrafi, A. Elbour, and M. Moussa
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 17 Dec 2013 11:24:35 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some characterizations of almost
limited sets and applications" by N. Machrafi, A. Elbour, and M. Moussa.
Abstract: Recently, J.X. Chen et al. introduced and studied the class of
almost limited sets in Banach lattices. In this paper we establish some
characterizations of almost limited sets in Banach lattices (resp. wDP*
property of Banach lattices), that generalize some results obtained by
J.X. Chen et al.. Also, we introduce and study the class of the almost
limited operators, which maps the closed unit bull of a Banach space
to an almost limited subset of a Banach lattice. Some results about
the relationship between the class of almost limited operators and that
of L-weakly compact (resp. M-weakly compact, resp. compact) operators
are presented.
Archive classification: math.FA
Mathematics Subject Classification: 46B42 (Primary) 46B50, 47B65
(Secondary)
Remarks: 9 pages
Submitted from: azizelbour at hotmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.2770
or
http://arXiv.org/abs/1312.2770
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Eytyhios Glakousakis and Sophocles
Mercourakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 17 Dec 2013 11:26:25 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the existence of 1-separated
sequences on the unit ball of a finite dimensional Banach space" by
Eytyhios Glakousakis and Sophocles Mercourakis.
Abstract: Given a finite dimensional Banach space X with dimX = n and
an Auerbach basis of X, it is proved that: there exists a set D of n +
1 linear combinations (with coordinates 0, -1, +1) of the members of
the basis, so that each pair of different elements of D have distance
greater than one.
Archive classification: math.FA math.CO math.MG
Submitted from: smercour at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.2896
or
http://arXiv.org/abs/1312.2896
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Elizabeth S. Meckes and Mark W. Meckes
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 17 Dec 2013 11:29:31 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the equivalence of modes of
convergence for log-concave measures" by Elizabeth S. Meckes and Mark
W. Meckes.
Abstract: An important theme in recent work in asymptotic geometric
analysis is that many classical implications between different types
of geometric or functional inequalities can be reversed in the presence
of convexity assumptions. In this note, we explore the extent to which
different notions of distance between probability measures are comparable
for log-concave distributions. Our results imply that weak convergence
of isotropic log-concave distributions is equivalent to convergence in
total variation, and is further equivalent to convergence in relative
entropy when the limit measure is Gaussian.
Archive classification: math.PR math.FA
Submitted from: mark.meckes at case.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.3094
or
http://arXiv.org/abs/1312.3094
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by R. Lechner and M. Passenbrunner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 17 Dec 2013 11:31:10 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Adaptive deterministic dyadic
grids on spaces of homogeneous type" by R. Lechner and M. Passenbrunner.
Abstract: In the context of spaces of homogeneous type, we develop a
method to deterministically construct dyadic grids, specifically adapted
to a given combinatorial situation. This method is used to estimate
vector--valued operators rearranging martingale difference sequences
such as the Haar system.
Archive classification: math.FA
Mathematics Subject Classification: 46E40
Remarks: 18 pages, 2 figures
Submitted from: lechner at bayou.uni-linz.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.3490
or
http://arXiv.org/abs/1312.3490
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Dongyang Chen, Lei Li and Bentuo Zheng
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 17 Dec 2013 11:32:54 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Perturbations of frames" by
Dongyang Chen, Lei Li and Bentuo Zheng.
Abstract: In this paper, we give some sufficient conditions under which
perturbations preserve Hilbert frames and near-Riesz bases. Similar
results are also extended to frame sequences, Riesz sequences and Schauder
frames. It is worth mentioning that some of our perturbation conditions
are quite different from those used in the previous literatures on
this topic.
Archive classification: math.FA
Remarks: to appear in Acta MAth. Sinica, English Series
Submitted from: leilee at nankai.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.3460
or
http://arXiv.org/abs/1312.3460
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Shahar Mendelson
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 17 Dec 2013 11:34:30 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A remark on the diameter of random
sections of convex bodies" by Shahar Mendelson.
Abstract: We obtain a new upper estimate on the Euclidean diameter of
the intersection of the kernel of a random matrix with iid rows with a
given convex body. The proof is based on a small-ball argument rather
than on concentration and thus the estimate holds for relatively general
matrix ensembles.
Archive classification: math.FA
Submitted from: shahar.mendelson at anu.edu.au
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.3608
or
http://arXiv.org/abs/1312.3608
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Paolo Dulio, Richard J. Gardner and Carla
Peri
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 17 Dec 2013 11:36:06 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Characterizing the dual mixed
volume via additive functionals" by Paolo Dulio, Richard J. Gardner and
Carla Peri.
Abstract: Integral representations are obtained of positive additive
functionals on finite products of the space of continuous functions (or
of bounded Borel functions) on a compact Hausdorff space. These are shown
to yield characterizations of the dual mixed volume, the fundamental
concept in the dual Brunn-Minkowski theory. The characterizations are
shown to be best possible in the sense that none of the assumptions
can be omitted. The results obtained are in the spirit of a similar
characterization of the mixed volume in the classical Brunn-Minkowski
theory, obtained recently by Milman and Schneider, but the methods
employed are completely different.
Archive classification: math.FA math.MG
Mathematics Subject Classification: Primary: 52A20, 52A30, secondary:
52A39, 52A41
Submitted from: Richard.Gardner at wwu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.4072
or
http://arXiv.org/abs/1312.4072
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Elisabeth M. Werner and Turkay Yolcu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 17 Dec 2013 11:38:08 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Equality characterization and
stability for entropy inequalities" by Elisabeth M. Werner and Turkay
Yolcu.
Abstract: We characterize the equality case in a recently established
entropy inequality. To do so, we show that characterization of equality
is equivalent to uniqueness of the solution of a certain Monge Ampere
differential equation. We prove the uniqueness of the solution using
methods from mass transport, due to Brenier, and Gangbo-McCann.
We then give stability versions for this entropy inequality, as well as
for a reverse log Sobolev inequality and for the L_p-affine isoperimetric
inequalities for both, log concave functions and convex bodies. In the
case of convex bodies such stability results have only been known in all
dimensions for p=1 and for p > 1 only for 0-symmetric bodies in the plane.
Archive classification: math.FA
Submitted from: elisabeth.werner at case.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.4148
or
http://arXiv.org/abs/1312.4148
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Informal Analysis Seminar at Kent State University,
1st-2nd March 2014
Date: Mon, 23 Dec 2013 15:42:35 +0000
From: Benjamin Jaye <bjaye at kent.edu>
To: banach at math.okstate.edu
Dear Colleague,
The Department of Mathematics at Kent State University is happy to announce
a meeting of the Kent State Informal Analysis Seminar. The Informal
Analysis Seminar will be held on March 1-2, 2014. The plenary lecture
series will be given by:
Svetlana Jitomirskaya (UC Irvine), and
Nets Katz (Caltech)
Each speaker will deliver a four hour lecture series designed to be
accessible for graduate students.
The conference is supported by the NSF. Funding is available to cover the
local expenses, and possibly travel expenses, of a limited number of
participants. Graduate students, postdoctoral researchers, and members of
underrepresented groups are particularly encouraged to apply for support.
Further information, and an online registration form, can be found online
at www.math.kent.edu/informal. Please feel free to contact us at
informal at math.kent.edu for any further information.
Attached is a poster that you are welcome to forward to any colleagues you
think may be interested.
Sincerely,
The analysis group at Kent State University.
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