Messages from 2007
These are the messages distributed to the Banach list during 2007.
From alspach at www.math.okstate.edu Tue Jan 2 21:38:50 2007
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Date: Tue, 2 Jan 2007 21:38:50 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200701030338.l033codO098489 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Bernhard Lamel
Status: R
This is an announcement for the paper "Local automorphisms of the
Hilbert ball" by Bernhard Lamel.
Abstract: We prove an analogue of Alexander's Theorem for holomorphic
mappings of the unit ball in a complex Hilbert space: Every holomorphic
mapping which takes a piece of the boundary of the unit ball into
the boundary of the unit ball and whose differential at some point
of this boundary is onto is the restriction of an automorphism of
the ball. We also show that it is enough to assume that the mapping
is only Gateaux-holomorphic.
Archive classification: Complex Variables; Functional Analysis
Mathematics Subject Classification: 32H12, 46G20, 46T25, 58C10
The source file(s), L_hilbertball/definitions.tex: 3255 bytes,
L_hilbertball/hilbertball2.bbl: 1011 bytes, L_hilbertball/hilbertball2.tex:
24133 bytes, is(are) stored in gzipped form as 0612688.tar.gz with
size 10kb. The corresponding postcript file has gzipped size 89kb.
Submitted from: bernhard.lamel at univie.ac.at
The paper may be downloaded from the archive by web browser from
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http://front.math.ucdavis.edu/math.CV/0612688
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From alspach at www.math.okstate.edu Tue Jan 2 21:39:38 2007
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Tue, 2 Jan 2007 21:39:37 -0600 (CST)
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Date: Tue, 2 Jan 2007 21:39:37 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200701030339.l033dbPN098520 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by J. Talponen
Status: R
This is an announcement for the paper "On weakly extremal structures
in Banach spaces" by J. Talponen.
Abstract: This paper deals with the interplay of the geometry of
the norm and the weak topology in Banach spaces. Both dual and
intrinsic connections between weak forms of rotundity and smoothness
ared discussed. Weakly exposed points, weakly locally uniformly
rotund spaces, smoothness, duality and the interplay of all the
above are studied. An example of a Banach space, which is midpoint
locally uniformly rotund but not weakly locally uniformly rotund
is given.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20; 46A20
Remarks: 12 pages
The source file(s), wg.tex: 45886 bytes, is(are) stored in gzipped
form as 0701009.gz with size 13kb. The corresponding postcript file
has gzipped size 103kb.
Submitted from: talponen at cc.helsinki.fi
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0701009
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From alspach at www.math.okstate.edu Wed Jan 10 15:26:06 2007
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Wed, 10 Jan 2007 15:26:06 -0600 (CST)
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Date: Wed, 10 Jan 2007 15:26:06 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200701102126.l0ALQ6s9056535 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Peter G. Casazza and Janet C. Tremain
Status: R
This is an announcement for the paper "the paving conjecture is
equivalent to the paving conjecture for triangular matrices" by
Peter G. Casazza and Janet C. Tremain.
Abstract: We resolve a 25 year old problem by showing that
The Paving Conjecture is equivalent to The Paving Conjecture for
Triangular
Matrices.
Archive classification: Functional Analysis
Mathematics Subject Classification: 47A20, 47B99, 46B07
The source file(s), 12.5.06.tex: 20512 bytes, is(are) stored in
gzipped form as 0701101.gz with size 7kb. The corresponding postcript
file has gzipped size 87kb.
Submitted from: pete at math.missouri.edu
The paper may be downloaded from the archive by web browser from
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http://front.math.ucdavis.edu/math.FA/0701101
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From alspach at www.math.okstate.edu Wed Jan 10 15:27:21 2007
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Date: Wed, 10 Jan 2007 15:27:21 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200701102127.l0ALRLZc056567 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Shachar Lovett and Sasha Sodin
Status: R
This is an announcement for the paper "Almost Euclidean sections
of the N-dimensional cross-polytope using O(N) random bits" by
Shachar Lovett and Sasha Sodin.
Abstract: It is well known that R^N has subspaces of dimension
proportional to N on which the \ell_1 norm is equivalent to the
\ell_2 norm; however, no explicit constructions are known. Extending
earlier work by Artstein--Avidan and Milman, we prove that such a
subspace can be generated using O(N) random bits.
Archive classification: Functional Analysis; Metric Geometry;
Probability
Remarks: 16 pages
The source file(s), derand.tex: 32081 bytes, is(are) stored in
gzipped form as 0701102.gz with size 11kb. The corresponding postcript
file has gzipped size 109kb.
Submitted from: sodinale at post.tau.ac.il
The paper may be downloaded from the archive by web browser from
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http://front.math.ucdavis.edu/math.FA/0701102
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From alspach at www.math.okstate.edu Fri Jan 12 10:28:50 2007
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Date: Fri, 12 Jan 2007 10:28:50 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200701121628.l0CGSo5e070481 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Boris Rubin
Status: R
This is an announcement for the paper "The lower dimensional
Busemann-Petty problem for bodies with the generalized axial
symmetry" by Boris Rubin.
Abstract: The lower dimensional Busemann-Petty problem asks, whether
$n$-dimensional origin-symmetric convex bodies, having smaller
$i$-dimensional sections, necessarily have smaller volumes.
For $i=1$, the affirmative answer is obvious. For $i>3$, the answer
is negative.
For $i=2$ and $i=3$, the problem is still open, except when the body
with smaller sections is a body of revolution. In this case the answer is
affirmative. The paper contains a complete solution to the problem
in the more general situation, when the body with smaller sections
is invariant under orthogonal transformations preserving coordinate
subspaces $R^{l}$ and $R^{n-l}$ of $R^{n}$ for arbitrary fixed
$0<l<n$.
Archive classification: Functional Analysis
Mathematics Subject Classification: 44A12; 52A38
Remarks: 26 pages
The source file(s), simplex2.tex: 72011 bytes, is(are) stored in
gzipped form as 0701317.gz with size 23kb. The corresponding postcript
file has gzipped size 155kb.
Submitted from: borisr at math.lsu.edu
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From alspach at www.math.okstate.edu Fri Jan 12 10:29:21 2007
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Date: Fri, 12 Jan 2007 10:29:21 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200701121629.l0CGTLEc070512 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by E. Odell and Th. Schlumprecht
Status: R
This is an announcement for the paper "Embedding into Banach spaces
with finite dimensional decompositions" by E. Odell and Th.
Schlumprecht.
Abstract: This paper deals with the following types of problems:
Assume a Banach space $X$ has some property (P). Can it be embedded
into some Banach space $Z$ with a finite dimensional decomposition
having property (P), or more generally, having a property related
to (P)? Secondly, given a class of Banach spaces, does there exist
a Banach space in this class, or in a closely related one, which
is universal for this class?
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B03; 46B20
Remarks: 26 pages
The source file(s), os-embedding-final.tex: 109527 bytes, is(are)
stored in gzipped form as 0701324.gz with size 33kb. The corresponding
postcript file has gzipped size 182kb.
Submitted from: combs at mail.ma.utexas.edu
The paper may be downloaded from the archive by web browser from
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http://front.math.ucdavis.edu/math.FA/0701324
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From alspach at www.math.okstate.edu Tue Jan 16 07:08:16 2007
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Date: Tue, 16 Jan 2007 07:08:16 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200701161308.l0GD8GnS098438 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by George Androulakis and Frank Sanacory
Status: R
This is an announcement for the paper "On the ``Multiple of the
Inclusion Plus Compact'' problem" by George Androulakis and Frank
Sanacory.
Abstract: The ``multiple of the inclusion plus compact problem''
which was posed by T.W.~Gowers in 1996 and Th.~Schlumprecht in 2003,
asks whether for every infinite dimensional Banach space $X$ there
exists a closed subspace $Y$ of $X$ and a bounded linear operator
from $Y$ to $X$ which is not a compact perturbation of a multiple
of the inclusion map from $Y$ to $X$. We give sufficient conditions
on the spreading models of seminormalized basic sequences of a
Banach space $X$ which guarantee that the ``multiple of the inclusion
plus compact'' problem has an affirmative answer for $X$. Our results
strengthen a previous result of the first named author, E.~Odell,
Th.~Schlumprecht and N.~Tomczak-Jaegermann as well as a result of
Th.~Schlumprecht. We give an example of a Hereditarily Indecomposable
Banach space where our results apply. For the proof of our main
result we use an extension of E.~Odell's Schreier unconditionality
result for arrays.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46A32, 47B07
The source file(s), lambdaipluscpt.tex: 114786 bytes, is(are) stored
in gzipped form as 0701354.gz with size 28kb. The corresponding
postcript file has gzipped size 203kb.
Submitted from: giorgis at math.sc.edu
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From alspach at www.math.okstate.edu Tue Jan 23 06:53:02 2007
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Date: Tue, 23 Jan 2007 06:53:02 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200701231253.l0NCr2Kq050489 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Peter G. Casazza, Dan Edidin, Deepti Kalra and Vern I. Paulsen
Status: R
This is an announcement for the paper "Projections and the
Kadison-Singer Problem" by Peter G. Casazza, Dan Edidin, Deepti
Kalra and Vern I. Paulsen.
Abstract: We prove some new equivalences of the paving conjecture
and obtain some estimates on the paving constants. In addition we
give a new family of counterexamples to one of the Akemann-Anderson
conjectures.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46L15; 47L25
The source file(s), 127.Projks.tex: 48714 bytes, is(are) stored in
gzipped form as 0701450.gz with size 16kb. The corresponding postcript
file has gzipped size 123kb.
Submitted from: pete at math.missouri.edu
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0701450
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From alspach at www.math.okstate.edu Tue Jan 23 06:53:53 2007
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Date: Tue, 23 Jan 2007 06:53:53 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200701231253.l0NCrrEm050521 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Marius Junge, Niels Jorgen Nielsen and Timur Oikhberg
Status: R
This is an announcement for the paper "Rosenthal operator spaces"
by Marius Junge, Niels Jorgen Nielsen and Timur Oikhberg.
Abstract: In 1969 Lindenstrauss and Rosenthal showed that if a
Banach space is isomorphic to a complemented subspace of an L_p-space,
then it is either a script L_p-space or isomorphic to a Hilbert
space. This is the motivation of this paper where we study
non--Hilbertian complemented operator subspaces of non commutative
L_p-spaces and show that this class is much richer than in the
commutative case. We investigate the local properties of some new
classes of operator spaces for every $2<p< \infty$ which can be
considered as operator space analogues of the Rosenthal sequence
spaces from Banach space theory, constructed in 1970. Under the
usual conditions on the defining sequence sigma we prove that most
of these spaces are operator script L_p-spaces, not completely
isomorphic to previously known such spaces. However it turns out
that some column and row versions of our spaces are not operator
script L_p-spaces and have a rather complicated local structure
which implies that the Lindenstrauss--Rosenthal alternative does
not carry over to the non-commutative case.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20;46L07;46L52
The source file(s), njnpart1new11.tex: 38162 bytes, njnpart2new11.tex:
48325 bytes, refnew11.tex: 4840 bytes, rosmatrixnew11.tex: 10401
bytes, uncomp2.tex: 6528 bytes, x3njn1111.tex: 5668 bytes, is(are)
stored in gzipped form as 0701480.tar.gz with size 33kb. The
corresponding postcript file has gzipped size 176kb.
Submitted from: njn at imada.sdu.dk
The paper may be downloaded from the archive by web browser from
URL
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From alspach at www.math.okstate.edu Tue Jan 30 10:52:52 2007
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Date: Tue, 30 Jan 2007 10:52:52 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200701301652.l0UGqqPg004666 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Emanuel Milman
Status: R
This is an announcement for the paper "A solution to a question of
A. Koldobsky" by Emanuel Milman.
Abstract: In 2000, A. Koldobsky asked whether two types of
generalizations of the notion of an intersection-body, are in fact
equivalent. The structures of these two types of generalized
intersection-bodies have been studied by the author in
[http://www.arxiv.org/math.MG/0512058], providing substantial
positive evidence for a positive answer to this question. The purpose
of this note is to construct a counter-example, which provides a
surprising negative answer to this question in a strong sense. This
negative answer implies the existence of a non-trivial non-negative
function in the range of the spherical Radon transform.
Archive classification: Functional Analysis
Remarks: 13 pages
The source file(s), Solution-To-Koldobsky-Question.bbl: 5474 bytes,
Solution-To-Koldobsky-Question.tex: 41825 bytes, is(are) stored in
gzipped form as 0701779.tar.gz with size 14kb. The corresponding
postcript file has gzipped size 110kb.
Submitted from: emanuel.milman at weizmann.ac.il
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http://front.math.ucdavis.edu/math.FA/0701779
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http://arXiv.org/abs/math.FA/0701779
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From alspach at www.math.okstate.edu Thu Feb 1 13:31:11 2007
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Date: Thu, 1 Feb 2007 13:31:10 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200702011931.l11JVASR020734 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Ludvek Zajivcek
Status: R
This is an announcement for the paper "On Lipschitz and d.c. surfaces
of finite codimension in a Banach space" by Ludvek Zajivcek.
Abstract: Properties of Lipschitz and d.c. surfaces of finite
codimension in a Banach space, and properties of generated
$\sigma$-ideals are studied. These $\sigma$-ideals naturally appear
in the differentiation theory and in the abstract approximation
theory. Using these properties, we improve an unpublished
result of M. Heisler which gives an alternative proof of a result
of D. Preiss on singular points of convex functions.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46T05, 58C20, 47H05
Remarks: 13 pages
The source file(s), ZAJICEK2.TEX: 48703 bytes, is(are) stored in
gzipped form as 0701926.gz with size 15kb. The corresponding postcript
file has gzipped size 99kb.
Submitted from: zajicek at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from
URL
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Date: Thu, 1 Feb 2007 14:36:04 -0600 (CST)
From: Bill Johnson <johnson at math.tamu.edu>
To: banach at math.okstate.edu
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Subject: [Banach] Workshop in Analysis and Probability at A&M
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Status: R
Workshop in Analysis and Probability
Department of Mathematics
Texas A&M University
Summer 2007
The Summer 2007 session of the Workshop in Analysis and Probability at
Texas A&M University will be in session from July 9 until August 12. For
information about the Workshop, consult the Workshop Home Page, URL
http://www.math.tamu.edu/research/workshops/linanalysis/
The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held
August 10-12. Speakers will include Rodrigo Banuelos, Grahame Bennett,
Dmitry Panchenko, Michael Steele, and Staszek Szarek.
Ken Dykema <kdykema at math.tamu.edu> and Michael Anshelevich
<manshel at math.tamu.edu> are organizing a Concentration Week on "Free
Probability Theory" which is designed to introduce advanced graduate
students and postdocs to Free Probability. It will take place July 9-13.
There will be one or two basic talks at the start for those without any
previous knowledge of free probability theory. Then lecture series will
be given by the following experts: Hari Bercovici, "Complex analytic and
probabalistic aspects of free probability theory"; Kenley Jung, "Free
entropy and operator algebras"; Alexandru Nica, "Combinatorics of free
probability theory".
Gideon Schechtman <gideon.schechtman at weizmann.ac.il> and Joel Zinn
<jzinn at math.tamu.edu> are organizing a Concentration Week on "Probability
Inequalities with Applications to High Dimensional Phenomena" that will
take place August 6 - August 10. The first day will be devoted to
introductory talks designed to introduce non experts to the subject.
The Workshop is supported in part by grants from the National Science
Foundation (NSF). Minorities, women, graduate students, and young
researchers are especially encouraged to attend.
For logistical support, including requests for support, please contact
Cara Barton <cara at math.tamu.edu> or Jaime Vykukal <jaime at math.tamu.edu>.
For more information on the Workshop itself, please contact William
Johnson <johnson at math.tamu.edu>, David Larson <larson at math.tamu.edu>,
Gilles Pisier <pisier at math.tamu.edu>, or Joel Zinn <jzinn at math.tamu.edu>.
For information about the Concentration Week "Free Probability Theory"
contact Michael Anshelevich <manshel at math.tamu.edu> or Ken Dykema
<kdykema at math.tamu.edu>.
For information about the Concentration Week on "Probability Inequalities
with Applications to High Dimensional Phenomena", contact Joel Zinn
<jzinn at math.tamu.edu>.
_______________________________________________
Banach mailing list
Banach at math.okstate.edu
http://mail.math.okstate.edu/mailman/listinfo/banach
From alspach at www.math.okstate.edu Thu Feb 8 12:46:40 2007
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Date: Thu, 8 Feb 2007 12:46:40 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200702081846.l18IkeVv086712 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by W. B. Johnson and Bentuo Zheng
Status: R
This is an announcement for the paper "A characterization of subspaces
and quotients of reflexive Banach spaces with unconditional basis"
by W. B. Johnson and Bentuo Zheng.
Abstract: We prove that the dual or any quotient of a separable
reflexive Banach space with the unconditional tree property has the
unconditional tree property. Then we prove that a separable reflexive
Banach space with the unconditional tree property embeds into a
reflexive Banach space with an unconditional basis. This solves
several long standing open problems. In particular, it yields that
a quotient of a reflexive Banach space with an unconditional finite
dimensional decomposition embeds into a reflexive Banach space with
an unconditional basis.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B03
The source file(s), JZh10.tex: 38045 bytes, is(are) stored in gzipped
form as 0702199.gz with size 11kb. The corresponding postcript file
has gzipped size 96kb.
Submitted from: btzheng at math.tamu.edu
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0702199
or
http://arXiv.org/abs/math.FA/0702199
or by email in unzipped form by transmitting an empty message with
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From alspach at www.math.okstate.edu Fri Feb 9 06:42:51 2007
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Date: Fri, 9 Feb 2007 06:42:51 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200702091242.l19Cgpml092795 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Peter G. Casazza, Gitta Kutyniok, Darrin Speegle and Janet C. Tremain
Status: R
This is an announcement for the paper "A decomposition theorem for
frames and the Feichtinger conjecture" by Peter G. Casazza, Gitta
Kutyniok, Darrin Speegle and Janet C. Tremain.
Abstract: In this paper we study the Feichtinger Conjecture in frame
theory, which was recently shown to be equivalent to the 1959
Kadison-Singer Problem in $C^{*}$-Algebras. We will show that every
bounded Bessel sequence can be decomposed into two subsets each of
which is an arbitrarily small perturbation of a sequence with a
finite orthogonal decomposition. This construction is then used to
answer two open problems concerning the Feichtinger Conjecture: 1.
The Feichtinger Conjecture is equivalent to the conjecture that
every unit norm Bessel sequence is a finite union of frame sequences.
2. Every unit norm Bessel sequence is a finite union of sets each
of which is $\omega$-independent for $\ell_2$-sequences.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46C05; 42C15; 46L05
Remarks: 10 pages
The source file(s), Decomposition_PAMS_final.tex: 35701 bytes,
proc-l.cls: 2486 bytes, is(are) stored in gzipped form as 0702216.tar.gz
with size 12kb. The corresponding postcript file has gzipped size
89kb.
Submitted from: gitta.kutyniok at math.uni-giessen.de
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0702216
or
http://arXiv.org/abs/math.FA/0702216
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From alspach at www.math.okstate.edu Fri Feb 9 06:43:56 2007
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Date: Fri, 9 Feb 2007 06:43:56 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200702091243.l19ChumQ092826 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Denka Kutzarova, Denny Leung, Antonis Manoussakis and Wee Kee Tang
Status: R
This is an announcement for the paper "Minimality properties of
Tsirelson type spaces" by Denka Kutzarova, Denny Leung, Antonis
Manoussakis and Wee Kee Tang.
Abstract: In this paper, we study minimality properties of partly
modified mixed Tsirelson spaces. A Banach space with a normalized
basis (e_k) is said to be subsequentially minimal if for every
normalized block basis (x_k) of (e_k), there is a further block
(y_k) of (x_k) such that (y_k) is equivalent to a subsequence of
(e_k). Sufficient conditions are given for a partly modified mixed
Tsirelson space to be subsequentially minimal and connections with
Bourgain's \ell^{1}-index are established. It is also shown that a
large class of mixed Tsirelson spaces fails to be subsequentially
minimal in a strong sense.
Archive classification: Functional Analysis
The source file(s), SubseqMinimal8A.tex: 107238 bytes, is(are)
stored in gzipped form as 0702210.gz with size 27kb. The corresponding
postcript file has gzipped size 176kb.
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/math.FA/0702210
or
http://arXiv.org/abs/math.FA/0702210
or by email in unzipped form by transmitting an empty message with
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uget 0702210
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From alspach at www.math.okstate.edu Fri Feb 9 06:45:18 2007
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Date: Fri, 9 Feb 2007 06:45:18 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200702091245.l19CjIr0092890 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Limor Ben-Efraim and Francoise Lust-Piquard
Status: R
This is an announcement for the paper "Poincar\'{e} type inequalities
on the discrete cube and in the CAR algebra" by Limor Ben-Efraim
and Francoise Lust-Piquard.
Abstract: We prove Lp Poincare inequalities for functions on the
discrete cube and their discrete gradient. We thus recover an
exponential inequality and the concentration phenomenon for the
uniform probability on the cube first obtained by Bobkov and Gotze.
Inequalities involving the discrete gradient and powers of the
discrete Laplacian are also considered, for the Lp norm or more
general ones. Similar results hold true, replacing functions on the
cube by elements of the CAR algebra and considering the annihilation
operators and the number operator.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46E39, 46L57, 46L51
The source file(s), poincare-cube-final.tex: 85518 bytes, is(are)
stored in gzipped form as 0702233.gz with size 21kb. The corresponding
postcript file has gzipped size 182kb.
Submitted from: limor_be at cs.huji.ac.il
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0702233
or
http://arXiv.org/abs/math.FA/0702233
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uget 0702233
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From alspach at www.math.okstate.edu Mon Feb 12 22:59:25 2007
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(envelope-from alspach)
Date: Mon, 12 Feb 2007 22:59:25 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200702130459.l1D4xPqm020018 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Florent Baudier and Gilles Lancien
Status: R
This is an announcement for the paper "Embeddings of locally finite
metric spaces into Banach spaces" by Florent Baudier and Gilles
Lancien.
Abstract: We show that if X is a Banach space without cotype, then
every locally finite metric space embeds metrically into X.
Archive classification: Metric Geometry; Functional Analysis
Mathematics Subject Classification: 46B20; 51F99
Remarks: 6 pages, to appear in Proceedings of the AMS
The source file(s), baudierlancien-final2.tex: 15038 bytes, is(are)
stored in gzipped form as 0702266.gz with size 5kb. The corresponding
postcript file has gzipped size 75kb.
Submitted from: florent.baudier at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.MG/0702266
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http://arXiv.org/abs/math.MG/0702266
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From alspach at www.math.okstate.edu Tue Feb 20 09:57:20 2007
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Date: Tue, 20 Feb 2007 09:57:20 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200702201557.l1KFvKBg076081 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Zhenglu Jiang and Xiaoyong Fu
Status: R
This is an announcement for the paper "The weak Banach-Saks Property
of the Space $(L_\mu^p)^m$" by Zhenglu Jiang and Xiaoyong Fu.
Abstract: In this paper we show the weak Banach-Saks property of
the Banach vector space $(L_\mu^p)^m$ generated by $m$ $L_\mu^p$-spaces
for $1\leq p<+\infty,$ where $m$ is any given natural number. When
$m=1,$ this is the famous Banach-Saks-Szlenk theorem. By use of
this property, we also present inequalities for integrals of functions
that are the composition of nonnegative continuous convex functions
on a convex set of a vector space ${\bf R}^m$ and vector-valued
functions in a weakly compact subset of the space $(L_\mu^p)^m$ for
$1\leq p<+\infty$ and inequalities when these vector-valued functions
are in a weakly* compact subset of the product space $(L_\mu^\infty)^m$
generated by $m$ $L_\mu^\infty$-spaces.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20, 40H05, 40G05, 47F05
Remarks: 7
The source file(s), jf-bs.tex: 29847 bytes, is(are) stored in gzipped
form as 0702537.gz with size 8kb. The corresponding postcript file
has gzipped size 104kb.
Submitted from: mcsjzl at mail.sysu.edu.cn
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0702537
or
http://arXiv.org/abs/math.FA/0702537
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From alspach at www.math.okstate.edu Tue Feb 20 09:58:43 2007
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Date: Tue, 20 Feb 2007 09:58:43 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200702201558.l1KFwh51076121 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Zhenglu Jiang and Xiaoyong Fu
Status: R
This is an announcement for the paper "The Banach-Saks Property of
the Banach product spaces" by Zhenglu Jiang and Xiaoyong Fu.
Abstract: In this paper we first take a detail survey of the study
of the Banach-Saks property of Banach spaces and then show the
Banach-Saks property of the product spaces generated by a finite
number of Banach spaces having the Banach-Saks property. A more
general inequality for integrals of a class of composite functions
is also given by using this property.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20, 40H05, 40G05, 47F05
Remarks: 6
The source file(s), bs0206.tex: 25085 bytes, is(are) stored in
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Submitted from: mcsjzl at mail.sysu.edu.cn
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0702538
or
http://arXiv.org/abs/math.FA/0702538
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From banach-bounces at math.okstate.edu Wed Feb 21 20:56:12 2007
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Date: Wed, 21 Feb 2007 20:56:07 -0600
From: Dale Alspach <alspach at math.okstate.edu>
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Subject: [Banach] Call for papers for Banach J. Math.
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Call for Papers for Banach J. Math.
[apologies for multiple postings]
Dear ISDE Members,
It is my pleasure to invite you most cordially to submit your original
research papers or critical survey articles (within the scope of the
Journal) for possible publication in "Banach Journal of Mathematics (BJM)"
and to promote our journal among your fellow-workers and colleagues. A
publishing of your paper will contribute so much for the success of the
journal. Following (and attached), kindly find more information about
how/where to submit a paper.
<a href="./Call_for_Papers_for_Banach_J._Math.pdf">Call_for_Papers_for_Banach_J._Math.pdf</a>
Kindly visit: http://www.math-analysis.org (an updated mirror)
We are looking forward to receiving your contributions in the style file
of BJM.
Sincerely yours
Mohammad Sal Moslehian
Editor-in-chief of BJM
Address: Department of Mathematics, P. O. Box 1159, Ferdowsi University,
Mashhad 91775, Iran
Tel-Fax: (+98)(511)(8828606)
Fax: (+98)(511)(8828609)
E-mail: moslehian at member.ams.org
Home: http://profsite.um.ac.ir/~moslehian/
http://www.math.okstate.edu/~alspach/banach/Call_for_Papers_for_Banach_J._Math.pdf
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Subject: [Banach] CONFERENCE ANNOUNCEMENT ICAT08
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Status: R
DEAR COLEAQUES HI!
PROFESSOR PAUL BUTZER OF AACHEN TECH.INST.,GERMANY,ONE OF THE MAIN
RESEARCHERS OF APPROXIMATION
THEORY AND MANY OTHER FIELDS, SUCH AS SAMPLING THEORY/SIGNAL
THEORY,FRACTIONAL
CALCULUS/ANALYSIS,OPERATORS,SEMIGROUPS,
CELEBRATES HIS 80TH BIRTHDAY IN 2008.
PROF.BUTZER STILL IS VERY ACTIVE IN RESEARCH AND IN EXCELLENT HEALTH.
TO HONOR HIM,HERE AT THE UNIV. OF MEMPHIS,TN,USA WE ORGANISE AN
INTERNATIONAL
CONFERENCE ON APPROXIMATION THEORY:ALL TOPICS, AND RELATED FIELDS ,SUCH
AS INEQUALITIES,FRACTIONAL
CALCULUS,FUZZY APPROX.TH,PROBABILISTIC APPROX.TH.,ETC.
THE CONFERENCE(ICAT08) WILL BE DURING OCTOBER 11-13,2008.
WE HOPE YOU COME,THERE WILL BE PROCEEDINGS.
THIS IS THE VERY FIRST ANNOUNCEMENT.THERE WILL BE A WEB SITE SOON.
AT THE MOMENT WE COLLECT ONLY INTEREST TO POSSIBLY COME.
PLEASE ANSWER US SOON IF YOU MAY BE COME.
THANKS
CORDIALLY
THE ORGANIZER
George A. Anastassiou,Ph.D
Professor of Mathematics
Department of Mathematical Sciences
The University of Memphis,Memphis,TN 38152,USA
Editor-In-Chief JoCAAA, JCAAM,JAFA ;World Sci.Publ.Book Series:
Concrete & Applicable Math.
Springer Consultant-Editor in computational math books
Birkhauser Consultant Editor in A.M.Sci.
CRC-A.M. Advisor
NOVA MATH books ADVISOR
ganastss at memphis.edu
http://www.eudoxuspress.com
http://www.msci.memphis.edu/~ganastss/jocaaa
http://www.msci.memphis.edu/~ganastss/jcaam
http://www.msci.memphis.edu/~ganastss/jafa
tel:(INT 001)- 901-678-3144 office
901-751-3553 home
901-678-2482 secr.
Fax: 901-678-2480
Associate Editor in:
J.Communications in Applied Analysis,
Inter.J.Applied Math.,Inter.J.Diff.Eq.&Appl.,CUBO,
J.Advances in non-linear Variational Inequalities,
e-J.of Inequalities in Pure and Applied Math.,
Anals U.Oradea-Fasciola Mathematica,
Archives of Inequalities and Applications,
Inter.J.of Pure&Appl.Math.,MIA,
Inter.J.of Computational and Numerical Analysis with Appl.
Honorary President of Soc.for study & promotion of
Ancient Greek Mathematics.
Honorary Editor Australian Journal of Mathematical Analysis and Appl.
Panamerican Mathematical Journal
Eudoxus Press,LLC Pres.
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From alspach at www.math.okstate.edu Sat Mar 10 13:58:13 2007
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Date: Sat, 10 Mar 2007 13:58:13 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200703101958.l2AJwDEH064774 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Stefan Neuwirth
Status: R
This is an announcement for the paper "The maximum modulus of a
trigonometric trinomial" by Stefan Neuwirth.
Abstract: Let Lambda be a set of three integers and let C_Lambda
be the space of 2pi-periodic functions with spectrum in Lambda
endowed with the maximum modulus norm. We isolate the maximum modulus
points x of trigonometric trinomials T in C_Lambda and prove that
x is unique unless |T| has an axis of symmetry. This permits to
compute the exposed and the extreme points of the unit ball of
C_Lambda, to describe how the maximum modulus of T varies with
respect to the arguments of its Fourier coefficients and to compute
the norm of unimodular relative Fourier multipliers on C_Lambda.
We obtain in particular the Sidon constant of Lambda.
Archive classification: Functional Analysis; Classical Analysis and
ODEs
Mathematics Subject Classification: MSC Primary 30C10, 42A05, 42A45,
46B20; Secondary 26D05, 42A55,
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0703236
or
http://arXiv.org/abs/math.FA/0703236
or by email in unzipped form by transmitting an empty message with
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uget 0703236
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From alspach at www.math.okstate.edu Wed Mar 21 15:19:21 2007
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Date: Wed, 21 Mar 2007 15:19:20 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200703212019.l2LKJKqb050246 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Mark Rudelson and Roman Vershynin
Status: R
This is an announcement for the paper "The Littlewood-Offord Problem
and invertibility of random matrices" by Mark Rudelson and Roman
Vershynin.
Abstract: We prove two basic conjectures on the distribution of the
smallest singular value of random n times n matrices with independent
entries. Under minimal moment assumptions, we show that the smallest
singular value is of order n^{-1/2}, which is optimal for Gaussian
matrices. Moreover, we give a optimal estimate on the tail probability.
This comes as a consequence of a new and essentially sharp estimate
in the Littlewood-Offord problem: for i.i.d. random variables X_k
and real numbers a_k, determine the probability P that the sum of
a_k X_k lies near some number v. For arbitrary coefficients a_k of
the same order of magnitude, we show that they essentially lie in
an arithmetic progression of length 1/p.
Archive classification: Probability; Functional Analysis
Mathematics Subject Classification: 15A52; 11P70
Remarks: 35 pages, no figures
Submitted from: vershynin at math.ucdavis.edu
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.PR/0703503
or
http://arXiv.org/abs/math.PR/0703503
or by email in unzipped form by transmitting an empty message with
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uget 0703503
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to: math at arXiv.org.
From alspach at www.math.okstate.edu Wed Mar 21 15:22:14 2007
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Date: Wed, 21 Mar 2007 15:22:13 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200703212022.l2LKMDSR050309 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Andrea Colesanti
Status: R
This is an announcement for the paper "From the Brunn-Minkowski
inequality to a class of Poincar\'e type inequalities" by Andrea
Colesanti.
Abstract: We present an argument which leads from the Brunn-Minkowski
inequality to a Poincare' type inequality on the boundary of convex
bodies with smooth boundary and positive Gauss curvature.
Archive classification: Functional Analysis; Metric Geometry
Mathematics Subject Classification: 52A20; 26D10
Remarks: 9 pages
The source file(s), testo.tex: 21763 bytes, is(are) stored in gzipped
form as 0703584.gz with size 7kb. The corresponding postcript file
has gzipped size 93kb.
Submitted from: colesant at math.unifi.it
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0703584
or
http://arXiv.org/abs/math.FA/0703584
or by email in unzipped form by transmitting an empty message with
subject line
uget 0703584
or in gzipped form by using subject line
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to: math at arXiv.org.
From alspach at www.math.okstate.edu Thu Mar 22 06:49:15 2007
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Date: Thu, 22 Mar 2007 06:49:15 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200703221149.l2MBnFej055407 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Dumitru Popa
Status: R
This is an announcement for the paper "Khinchin's inequality,
Dunford--Pettis and compact operators on the space $\pmb{C([0,1],X)}$"
by Dumitru Popa.
Abstract: We prove that if $X,Y$ are Banach spaces, $\Omega$ a
compact Hausdorff space and $U\hbox{\rm :}\ C(\Omega,X)\rightarrow
Y$ is a bounded linear operator, and if $U$ is a Dunford--Pettis
operator the range of the representing measure $G(\Sigma) \subseteq
DP(X,Y)$ is an uniformly Dunford--Pettis family of operators and
$\|G\|$ is continuous at $\emptyset$. As applications of this result
we give necessary and/or sufficient conditions that some bounded
linear operators on the space $C([0,1],X)$ with values in $c_{0}$
or $l_{p}$, ($1\leq p<\infty$) be Dunford--Pettis and/or compact
operators, in which, Khinchin's inequality plays an important role.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B28; 47A80; 47B10
Remarks: 18 pages
The source file(s), mat01.cls: 37299 bytes, mathtimy.sty: 20 bytes,
pm2710new.tex: 66481 bytes, is(are) stored in gzipped form as
0703626.tar.gz with size 24kb. The corresponding postcript file has
gzipped size 76kb.
Submitted from: dpopa at univ-ovidius.ro
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0703626
or
http://arXiv.org/abs/math.FA/0703626
or by email in unzipped form by transmitting an empty message with
subject line
uget 0703626
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From alspach at www.math.okstate.edu Tue Apr 10 07:02:30 2007
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(envelope-from alspach)
Date: Tue, 10 Apr 2007 07:02:30 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200704101202.l3AC2UwZ000661 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Boris Rubin
Status: R
This is an announcement for the paper "Intersection bodies and
generalized cosine transforms" by Boris Rubin.
Abstract: Intersection bodies represent a remarkable class of
geometric objects associated with sections of star bodies and
invoking Radon transforms, generalized cosine transforms, and the
relevant Fourier analysis. We review some known facts and give them
new proofs. The main focus is interrelation between generalized
cosine transforms of different kinds and their application to
investigation of certain family of intersection bodies, which we
call lambda-intersection bodies. The latter include k-intersection
bodies (in the sense of A. Koldobsky) and unit balls of finite-dimensional
subspaces of $L_p$-spaces. In particular, we show that restriction
of the spherical Radon transforms and the generalized cosine
transforms onto lower dimensional subspaces preserves their
integral-geometric structure. We apply this result to the study
of sections of lambda-intersection bodies. A number of new
characterizations of this class of bodies and examples are given.
Archive classification:
Mathematics Subject Classification: 44A12; 52A38
Remarks: 36 pages
The source file(s), , is(are) stored in gzipped form as 0704.0061.gz
with size 31kb. The corresponding postcript file has gzipped size
195kb.
Submitted from: borisr at math.lsu.edu
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/
or
http://arXiv.org/abs/
or by email in unzipped form by transmitting an empty message with
subject line
uget
or in gzipped form by using subject line
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to: math at arXiv.org.
From alspach at www.math.okstate.edu Tue Apr 10 07:03:20 2007
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(envelope-from alspach)
Date: Tue, 10 Apr 2007 07:03:19 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200704101203.l3AC3J6l000693 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jesus Araujo
Status: R
This is an announcement for the paper "Examples and counterexamples
of type I isometric shifts" by Jesus Araujo.
Abstract: We provide examples of nonseparable spaces $X$ for which
$C(X)$ admits an isometric shift of type I, which solves in the
negative a problem proposed by Gutek {\em et al.} (J. Funct. Anal.
{\bf 101} (1991), 97-119). We also give two independent methods for
obtaining separable examples. The first one allows us in particular
to construct examples with infinitely many nonhomeomorphic components
in a subset of the Hilbert space $\ell^2$. The second one applies
for instance to sequences adjoined to any $n$-dimensional compact
manifold (for $n \ge 2$) or to the Sierpi\'nski curve. The combination
of both techniques lead to different examples involving a convergent
sequence adjoined to the Cantor set: one method for the case when
the sequence converges to a point in the Cantor set, and the other
one for the case when it converges outside.
Archive classification: Functional Analysis; General Topology
Mathematics Subject Classification: Primary 47B38; Secondary 46E15,
47B33, 47B37, 54D65, 54H20
Remarks: 41 pages. No figures. AMS-LaTeX
The source file(s), shiftnum86.tex: 124237 bytes, is(are) stored
in gzipped form as 0703892.gz with size 34kb. The corresponding
postcript file has gzipped size 210kb.
Submitted from: araujoj at unican.es
The paper may be downloaded from the archive by web browser from
URL
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From alspach at www.math.okstate.edu Tue Apr 17 08:21:49 2007
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Date: Tue, 17 Apr 2007 08:21:49 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200704171321.l3HDLnYc054133 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Valentin Ferenczi and Eloi Medina Galego
Status: R
This is an announcement for the paper "Even infinite dimensional
real Banach spaces" by Valentin Ferenczi and Eloi Medina Galego.
Abstract: This article is a continuation of a paper of the first
author \cite{F} about complex structures on real Banach spaces. We
define a notion of even infinite dimensional real Banach space, and
prove that there exist even spaces, including HI or unconditional
examples from \cite{F} and $C(K)$ examples due to Plebanek \cite{P}.
We extend results of \cite{F} relating the set of complex structures
up to isomorphism on a real space to a group associated to inessential
operators on that space, and give characterizations of even spaces
in terms of this group. We also generalize results of \cite{F} about
totally incomparable complex structures to essentially incomparable
complex structures, while showing that the complex version of a
space defined by S. Argyros and A. Manoussakis \cite{AM} provide
examples of essentially incomparable complex structures which are
not totally incomparable.
Archive classification:math.FA
Mathematics Subject Classification: 46B03; 47A53.
Remarks: 22 pages
The source file(s), EvenBanachspaces.tex, is(are) stored in gzipped form as 0704.1459.gz
with size 16kb. The corresponding postcript file has gzipped size
85kb.
Submitted from: ferenczi at ccr.jussieu.fr
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From alspach at www.math.okstate.edu Tue Apr 17 08:22:26 2007
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Date: Tue, 17 Apr 2007 08:22:25 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200704171322.l3HDMPNb054177 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Florent Baudier
Status: R
This is an announcement for the paper "Metrical characterization
of super-reflexivity and linear type of Banach spaces" by Florent
Baudier.
Abstract: We prove that a Banach space X is not super-reflexive if
and only if the hyperbolic infinite tree embeds metrically into X.
We improve one implication of J.Bourgain's result who gave a metrical
characterization of super-reflexivity in Banach spaces in terms of
uniforms embeddings of the finite trees. A characterization of the
linear type for Banach spaces is given using the embedding of the
infinite tree equipped with a suitable metric.
Archive classification:
Mathematics Subject Classification: 46B20; 51F99
Remarks: to appear in Archiv der Mathematik
The source file(s), metric.tex, is(are) stored in gzipped form as 0704.1955.gz
with size 8kb. The corresponding postcript file has gzipped size
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Submitted from: florent.baudier at univ-fcomte.fr
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From alspach at www.math.okstate.edu Thu May 3 08:46:50 2007
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Date: Thu, 3 May 2007 08:46:50 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200705031346.l43Dko6h075108 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Daniel Freeman
Status: R
This is an announcement for the paper "Weakly null sequences with
upper estimates" by Daniel Freeman.
Abstract: We prove that if $(v_i)$ is a normalized basic sequence
and X is a Banach space such that every normalized weakly null
sequence in X has a subsequence that is dominated by $(v_i)$, then
there exists a uniform constant $C\geq1$ such that every normalized
weakly null sequence in X has a subsequence that is C-dominated by
$(v_i)$. This extends a result of Knaust and Odell, who proved this
for the cases in which $(v_i)$ is the standard basis for $\ell_p$
or $c_0$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20; 46B03, 46B10
Remarks: 21 pages
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form as 0705.0218.gz with size 20kb. The corresponding postcript
file has gzipped size 146kb.
Submitted from: freeman at math.tamu.edu
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From banach-bounces at math.okstate.edu Thu May 3 20:46:39 2007
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Date: Thu, 03 May 2007 20:46:36 -0500
From: Dale Alspach <alspach at math.okstate.edu>
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Subject: [Banach] History of Banach Spaces and Linear Operators
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Status: R
This is an announcement of the publication of the book
History of Banach Spaces and Linear Operators by Albrecht Pietsch
The table of contents and preface can be viewed here:
http://www.math.okstate.edu/~alspach/banach/pietsch-history.pdf
_______________________________________________
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From alspach at www.math.okstate.edu Sat May 19 22:48:47 2007
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Date: Sat, 19 May 2007 22:48:46 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200705200348.l4K3mk6C046121 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jarno Talponen
Status: R
This is an announcement for the paper "Convex-transitive characterizations
of Hilbert spaces" by Jarno Talponen.
Abstract: In this paper we investigate real convex-transitive Banach
spaces X, which admit a 1-dimensional bicontractive projection P
on X. Various mild conditions regarding the weak topology and the
geometry of the norm are provided, which guarantee that such an X
is in fact isometrically a Hilbert space. The results obtained can
be regarded as partial answers to the well-known Banach-Mazur
rotation problem, as well as to a question posed by B. Randrianantoanina
in 2002 about convex-transitive spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B04; 46C15
The source file(s), amsct2.tex: 89202 bytes, is(are) stored in
gzipped form as 0705.2526.gz with size 24kb. The corresponding
postcript file has gzipped size 142kb.
Submitted from: talponen at cc.helsinki.fi
The paper may be downloaded from the archive by web browser from
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From alspach at www.math.okstate.edu Sat May 19 22:51:19 2007
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Date: Sat, 19 May 2007 22:51:19 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200705200351.l4K3pJKX046172 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Han Ju Lee
Status: R
This is an announcement for the paper "Strong peak points and
denseness of strong peak functions" by Han Ju Lee.
Abstract: Let $C_b(K)$ be the set of all bounded continuous (real
or complex) functions on a complete metric space $K$ and $A$ a
closed subspace of $C_b(K)$. Using the variational method, it is
shown that the set of all strong peak functions in $A$ is dense if
and only if the set of all strong peak points is a norming subset
of $A$. As a corollary we show that if $X$ is a locally uniformly
convex, complex Banach space, then the set of all strong peak
functions in $\mathcal{A}(B_X)$ is a dense $G_\delta$ subset.
Moreover if $X$ is separable, smooth and locally uniformly convex,
then the set of all norm and numerical strong peak functions in
$\mathcal{A}_u(B_X:X)$ is a dense $G_\delta$ subset. In case that
a set of uniformly strongly exposed points of a (real or complex)
Banach space $X$ is a norming subset of $\mathcal{P}({}^n X)$ for
some $n\ge 1$, then the set of all strongly norm attaining elements
in $\mathcal{P}({}^n X)$ is dense, in particular, the set of all
points at which the norm of $\mathcal{P}({}^n X)$ is Fr\'echet
differentiable is a dense $G_\delta$ subset.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 46G20, 46G25, 46B22
The source file(s), variationalmethod-2007-04-15.tex: 25864 bytes,
is(are) stored in gzipped form as 0705.2650.gz with size 8kb. The
corresponding postcript file has gzipped size 75kb.
Submitted from: hahnju at postech.ac.kr
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From alspach at www.math.okstate.edu Wed May 30 08:34:44 2007
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Date: Wed, 30 May 2007 08:34:44 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200705301334.l4UDYis9054370 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by S.S. Kutateladze
Status: R
This is an announcement for the paper "Interaction of order and
convexity" by S.S. Kutateladze.
Abstract: This is an overview of merging the techniques of Riesz
space theory and convex geometry.
Archive classification: math.FA
Mathematics Subject Classification: 46B42; 52A39
Remarks: Prepared for the Russian--German geometry meeting dedicated
to the 95th anniversary of A. D. Alexandrov (1912--1999), St. Petersburg,
June 18--23, 2007
The paper may be downloaded from the archive by web browser from
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http://front.math.ucdavis.edu/0705.4124
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From alspach at www.math.okstate.edu Wed Jun 6 14:41:21 2007
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Date: Wed, 6 Jun 2007 14:41:20 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706061941.l56JfKEH030573 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Robert J Taggart
Status: R
This is an announcement for the paper "Pointwise convergence for
semigroups in vector-valued $L^p$ spaces" by Robert J Taggart.
Abstract: Suppose that T_t is a symmetric diffusion semigroup on
L^2(X). We show that the tensor extension of T_t to L^p(X;B), where
B belongs to a certain class of UMD spaces, exhibits pointwise
convergence almost everywhere as t approaches zero. Our principal
tools are vector-valued versions of maximal theorems due to
Hopf--Dunford--Schwartz and Stein. These are proved using subpositivity
and estimates on the bounded imaginary powers of the generator of
T_t. An extension of these results to analytic continuations of T_t
is also given.
Archive classification: math.FA math.SP
Mathematics Subject Classification: 47D03
The source file(s), ptwise_convergence_preprint.tex: 67741 bytes,
is(are) stored in gzipped form as 0705.4510.gz with size 19kb. The
corresponding postcript file has gzipped size 124kb.
Submitted from: r.taggart at unsw.edu.au
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From alspach at www.math.okstate.edu Wed Jun 6 14:47:33 2007
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Date: Wed, 6 Jun 2007 14:47:32 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706061947.l56JlWeu030637 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Gordan Zitkovic
Status: R
This is an announcement for the paper "A filtered version of the
bipolar theorem of Brannath and Schachermayer" by Gordan Zitkovic.
Abstract: We extend the Bipolar Theorem of Brannath and Schachermayer
(1999) to the space of nonnegative cadlag supermartingales on a
filtered probability space. We formulate the notion of fork-convexity
as an analogue to convexity in this setting. As an intermediate
step in the proof of our main result we establish a conditional
version of the Bipolar theorem. In an application to mathematical
finance we describe the structure of the set of dual processes of
the utility maximization problem of Kramkov and Schachermayer (1999)
and give a budget-constraint characterization of admissible consumption
processes in an incomplete semimartingale market.
Archive classification: math.PR math.FA
Citation: Journal of Theoretical Probability (2005) vol. 15 no. 1
The source file(s), Bipolar.tex: 58142 bytes, is(are) stored in
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From alspach at www.math.okstate.edu Wed Jun 6 14:52:14 2007
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Date: Wed, 6 Jun 2007 14:52:14 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706061952.l56JqE16030688 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Tim Austin, Assaf Naor, and Alain Valette
Status: R
This is an announcement for the paper "The Euclidean distortion of
the lamplighter group" by Tim Austin, Assaf Naor, and Alain Valette.
Abstract: We show that the cyclic lamplighter group $C_2 \bwr C_n$
embeds into Hilbert space with distortion ${\rm O}\left(\sqrt{\log
n}\right)$. This matches the lower bound proved by Lee, Naor and
Peres in~\cite{LeeNaoPer}, answering a question posed in that paper.
Thus the Euclidean distortion of $C_2 \bwr C_n$ is $\Theta\left(\sqrt{\log
n}\right)$. Our embedding is constructed explicitly in terms of the
irreducible representations of the group. Since the optimal Euclidean
embedding of a finite group can always be chosen to be equivariant,
as shown by Aharoni, Maurey and Mityagin~\cite{AhaMauMit} and by
Gromov (see~\cite{deCTesVal}), such representation-theoretic
considerations suggest a general tool for obtaining upper and lower
bounds on Euclidean embeddings of finite groups.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 46B20, 54E40, 52C99
The source file(s), LAMP-official.bbl: 3624 bytes
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From alspach at www.math.okstate.edu Wed Jun 6 14:55:31 2007
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Date: Wed, 6 Jun 2007 14:55:31 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706061955.l56JtVoJ030749 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Marius Junge and Javier Parcet
Status: R
This is an announcement for the paper "Operator space Lp embedding
theory I" by Marius Junge and Javier Parcet.
Abstract: Given any $1 < q \le 2$, we use new free probability
techniques to construct a completely isomorphic embedding of $\ell_q$
(equipped with its natural operator space structure) into the predual
of a sufficiently large QWEP von Neumann algebra.
Archive classification: math.OA math.PR
Mathematics Subject Classification: 46L07; 46L51; 46L52; 46L54
Remarks: This is the most accessible part of our paper Operator
space embedding of Lq into Lp, 28 pages.
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0706.0550
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http://arXiv.org/abs/0706.0550
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From alspach at www.math.okstate.edu Wed Jun 6 14:56:51 2007
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Date: Wed, 6 Jun 2007 14:56:51 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706061956.l56JupiS030781 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by L. Vesely and L. Zajicek
Status: R
This is an announcement for the paper "On compositions of d.c.
functions and mappings" by L. Vesely and L. Zajicek.
Abstract: A d.c. (delta-convex) function on a normed linear space
is a function representable as a difference of two continuous convex
functions. We show that an infinite dimensional analogue of Hartman's
theorem on stability of d.c. functions under compositions does not
hold in general. However, we prove that it holds in some interesting
particular cases. Our main results about compositions are proved
in the more general context of d.c. mappings between normed linear
spaces.
Archive classification: math.FA math.CA
Mathematics Subject Classification: 46B99; 26B25; 52A41
Remarks: 19 pages
The source file(s), PFzkr13.tex: 57750 bytes, is(are) stored in
gzipped form as 0706.0624.gz with size 18kb. The corresponding
postcript file has gzipped size 125kb.
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/0706.0624
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From alspach at www.math.okstate.edu Wed Jun 6 15:05:57 2007
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Date: Wed, 6 Jun 2007 15:05:57 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706062005.l56K5vrN030859 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by James R. Lee, Assaf Naor, and Yuval Peres
Status: R
This is an announcement for the paper "Trees and Markov convexity"
by James R. Lee, Assaf Naor, and Yuval Peres.
Abstract: We show that an infinite weighted tree admits a bi-Lipschitz
embedding into Hilbert space if and only if it does not contain
arbitrarily large complete binary trees with uniformly bounded
distortion. We also introduce a new metric invariant called Markov
convexity, and show how it can be used to compute the Euclidean
distortion of any metric tree up to universal factors.
Archive classification: math.MG math.FA
The source file(s), TreeMarkov-GAFA.tex: 228845 bytes
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0706.0545
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From alspach at www.math.okstate.edu Wed Jun 6 15:07:28 2007
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Date: Wed, 6 Jun 2007 15:07:28 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706062007.l56K7SxT030891 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by P. Holicky, O. Kalenda, L. Vesely, and L. Zajicek
Status: R
This is an announcement for the paper "Quotients of continuous
convex functions on nonreflexive Banach spaces" by P. Holicky, O.
Kalenda, L. Vesely, and L. Zajicek.
Abstract: On each nonreflexive Banach space X there exists a positive
continuous convex function f such that 1/f is not a d.c. function
(i.e., a difference of two continuous convex functions). This result
together with known ones implies that X is reflexive if and only
if each everywhere defined quotient of two continuous convex functions
is a d.c. function. Our construction gives also a stronger version
of Klee's result concerning renormings of nonreflexive spaces and
non-norm-attaining functionals.
Archive classification: math.FA
Mathematics Subject Classification: 46B10; 46B03
Remarks: 5 pages
The source file(s), 06HKVZscisly.tex: 19081 bytes, is(are) stored
in gzipped form as 0706.0633.gz with size 7kb. The corresponding
postcript file has gzipped size 71kb.
Submitted from: zajicek at karlin.mff.cuni.cz
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From alspach at www.math.okstate.edu Wed Jun 6 15:08:28 2007
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Date: Wed, 6 Jun 2007 15:08:28 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706062008.l56K8SYF030923 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Edward Odell, Thomas Schlumprecht and Andras Zsak
Status: R
This is an announcement for the paper "A new infinite game in Banach
spaces with applications" by Edward Odell, Thomas Schlumprecht and
Andras Zsak.
Abstract: We consider the following two-player game played on a
separable, infinite-dimensional Banach space X. Player S chooses a
positive integer k_1 and a finite-codimensional subspace X_1 of X.
Then player P chooses x_1 in the unit sphere of X_1. Moves alternate
thusly, forever. We study this game in the following setting. Certain
normalized, 1-unconditional sequences (u_i) and (v_i) are fixed so
that S has a winning strategy to force P to select x_i's so that
if the moves are (k_1,X_1,x_1,k_2,X_2,x_2,...), then (x_i) is
dominated by (u_{k_i}) and/or (x_i) dominates (v_{k_i}). In particular,
we show that for suitable (u_i) and (v_i) if X is reflexive and S
can win both of the games above, then X embeds into a reflexive
space Z with an FDD which also satisfies analogous block upper (u_i)
and lower (v_i) estimates. Certain universal space consequences
ensue.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 30 pages, uses mypreamble.tex
The source file(s), mypreamble.tex: 7670 bytes
The paper may be downloaded from the archive by web browser from
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From alspach at www.math.okstate.edu Thu Jun 21 08:05:24 2007
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Date: Thu, 21 Jun 2007 08:05:24 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706211305.l5LD5Ole035509 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Stanislaw Prus and Andrzej Wisnicki
Status: R
This is an announcement for the paper "On the fixed point property
in direct sums of Banach spaces with strictly monotone norms" by
Stanislaw Prus and Andrzej Wisnicki.
Abstract: It is shown that if a Banach space X has the super fixed
point property for nonexpansive mappings or admits a 1-unconditional
basis and Y satisfies property asymptotic (P) (which is weaker than
the condition WCS(Y)>1), then the direct sum of X and Y endowed
with a strictly monotone norm enjoys the weak fixed point property.
Archive classification: math.FA
Mathematics Subject Classification: 47H09; 46B20
Remarks: 12 pages
The source file(s), direct_p.tex: 35126 bytes, is(are) stored in
gzipped form as 0706.0915.gz with size 10kb. The corresponding
postcript file has gzipped size 86kb.
Submitted from: awisnic at golem.umcs.lublin.pl
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From alspach at www.math.okstate.edu Thu Jun 21 08:06:27 2007
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Date: Thu, 21 Jun 2007 08:06:27 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706211306.l5LD6RKx035540 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Chang-Pao Chen, Hao-Wei Huang, and Chun-Yen Shen
Status: R
This is an announcement for the paper "Characterization of the
matrix whose norm is determined by its action on decreasing
sequences" by Chang-Pao Chen, Hao-Wei Huang, and Chun-Yen Shen.
Abstract: Let $A=(a_{j,k})_{j,k \ge 1}$ be a non-negative matrix.
In this paper, we characterize those $A$ for which $\|A\|_{E, F}$
are determined by their actions on decreasing sequences, where $E$
and $F$ are suitable normed Riesz spaces of sequences.
Archive classification: math.FA
Mathematics Subject Classification: 15A60, 40G05, 47A30, 47B37
The source file(s), HWHshenfinal.tex: 34262 bytes, is(are) stored
in gzipped form as 0706.1098.gz with size 11kb. The corresponding
postcript file has gzipped size 96kb.
Submitted from: shenc at indiana.edu
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From alspach at www.math.okstate.edu Thu Jun 21 08:08:07 2007
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Date: Thu, 21 Jun 2007 08:08:07 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706211308.l5LD87u5035578 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Omer Friedland and Sasha Sodin
Status: R
This is an announcement for the paper "An extension of a
Bourgain--Lindenstrauss--Milman inequality" by Omer Friedland and
Sasha Sodin.
Abstract: Let || . || be a norm on R^n. Averaging || (\eps_1 x_1,
\cdots, \eps_n x_n) || over all the 2^n choices of \eps = (\eps_1,
\cdots, \eps_n) in \{ -1, +1 \}^n, we obtain an expression ||| .
||| which is an unconditional norm on R^n.
Bourgain, Lindenstrauss and Milman showed that, for a certain (large)
constant \eta > 1, one may average over (\eta n) (random) choices
of \eps and obtain a norm that is isomorphic to ||| . |||. We show
that this is the case for any \eta > 1.
Archive classification: math.FA math.PR
The source file(s), kkh_18.6.tex: 12943 bytes, is(are) stored in
gzipped form as 0706.2638.gz with size 5kb. The corresponding
postcript file has gzipped size 63kb.
Submitted from: sodinale at post.tau.ac.il
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From alspach at www.math.okstate.edu Thu Jun 21 08:09:13 2007
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Date: Thu, 21 Jun 2007 08:09:13 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706211309.l5LD9DY6035611 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Tim Austin, Assaf Naor, and Yuval Peres
Status: R
This is an announcement for the paper "The wreath product of Z with
Z has Hilbert compression exponent 2/3" by Tim Austin, Assaf Naor,
and Yuval Peres.
Abstract: We consider the wreath product $\Z\bwr \Z $, and prove
that any Lipschitz function $f:\Z\bwr \Z \to L_2$ satisfies
$$\liminf_{d_{\Z\bwr\Z}(x,y)\to
\infty}\frac{\|f(x)-f(y)\|_2}{d_{\Z\bwr\Z}(x,y)^{2/3}}<\infty. $$
On the other hand, as as shown by Tessera in~\cite{Tess06}, there
exists a Lipschitz function $g:\Z\bwr \Z \to L_2$ and a real $c>0$
such that $\|f(x)-f(y)\|_2 \ge c\,d_{\Z\bwr\Z}(x,y)^{2/3}$ for all
$x,y \in \Z\bwr\Z$. Thus the Hilbert compression exponent of $\Z\bwr
\Z$ is exactly $\frac23$, answering a question posed by Arzhantseva,
Guba and Sapir~\cite{AGS06} and by Tessara~\cite{Tess06}. Our proof
is based on an application of K. Ball's notion of Markov type.
Archive classification: math.MG math.FA
The source file(s), ZwreathZ.bbl: 3412 bytes
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From alspach at www.math.okstate.edu Thu Jun 28 10:46:55 2007
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Date: Thu, 28 Jun 2007 10:46:55 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706281546.l5SFkt4Z085045 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Valentin Ferenczi and Eloi Medina Galego
Status: R
This is an announcement for the paper "Countable groups of isometries
on Banach spaces" by Valentin Ferenczi and Eloi Medina Galego.
Abstract: A group $G$ is representable in a Banach space $X$ if $G$
is isomorphic to the group of isometries on $X$ in some equivalent
norm. We prove that a countable group $G$ is representable in a
separable real Banach space $X$ in several general cases, including
when $G=\{-1,1\} \times H$, $H$ finite and $\dim X \geq |H|$, or
when $G$ contains a normal subgroup with two elements and $X$ is
of the form $c_0(Y)$ or $\ell_p(Y)$, $1 \leq p <+\infty$. This is
a consequence of a result inspired by methods of S. Bellenot and
stating that under rather general conditions on a separable real
Banach space $X$ and a countable bounded group $G$ of isomorphisms
on $X$ containing $-Id$, there exists an equivalent norm on $X$ for
which $G$ is equal to the group of isometries on $X$.
We also extend methods of K. Jarosz to prove that any complex
Banach space of dimension at least $2$ may be renormed to admit
only trivial real isometries, and that any real Banach space which
is a cartesian square may be renormed to admit only trivial and
conjugation real isometries. It follows that every real space of
dimension at least $4$ and with a complex structure up to isomorphism
may be renormed to admit exactly two complex structures up to
isometry, and that every real cartesian square may be renormed to
admit a unique complex structure up to isometry.
Archive classification: math.FA
Mathematics Subject Classification: 46B03; 46B04
Remarks: 43 pages
The source file(s), ferenczigalego_isometries.tex: 104441 bytes,
is(are) stored in gzipped form as 0706.3861.gz with size 29kb. The
corresponding postcript file has gzipped size 137kb.
Submitted from: ferenczi at ccr.jussieu.fr
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From alspach at www.math.okstate.edu Thu Jun 28 11:00:28 2007
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Date: Thu, 28 Jun 2007 11:00:28 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706281600.l5SG0S2D085165 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jeff Cheeger and Bruce Kleiner
Status: R
This is an announcement for the paper "Characterizations of the
Radon-Nikodym Property in terms of inverse limits" by Jeff Cheeger
and Bruce Kleiner.
Abstract: We show that a separable Banach space has the Radon-Nikodym
Property if and only if it is isomorphic to the limit of an inverse
system, V_1<--- V_2<---...<--- V_k<---..., where the V_i's are
finite dimensional Banach spaces, and the bonding maps V_{k-1}<---
V_k are quotient maps. We also show that the inverse system can be
chosen to be a good finite dimensional approximation (GFDA), a
notion introduced our earlier paper "On the differentiability of
Lipschtz maps from metric measure spaces into Banach spaces". As a
corollary, it follows that the differentiation and bi-Lipschitz
non-embedding theorems in that paper, which were proved for maps
into GFDA targets, are optimal in the sense that they hold for
targets with the Radon-Nikodym Property.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B22;46G05
The source file(s), gfda.bbl: 1902 bytes
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0706.3389
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From alspach at www.math.okstate.edu Thu Jun 28 11:01:16 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200706281601.l5SG1FmR085201 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Han Ju Lee
Status: R
This is an announcement for the paper "Randomized series and geometry
of Banach spaces" by Han Ju Lee.
Abstract: We study some properties of the randomized series and
their applications to the geometric structure of Banach spaces. For
$n\ge 2$ and $1<p<\infty$, it is shown that $\ell_\infty^n$ is
representable in a Banach space $X$ if and only if it is representable
in the Lebesgue-Bochner $L_p(X)$. New criteria for various convexity
properties in Banach spaces are also studied. It is proved that a
Banach lattice $E$ is uniformly monotone if and only if its
$p$-convexification $E^{(p)}$ is uniformly convex and that a K\"othe
function space $E$ is upper locally uniformly monotone if and only
if its $p$-convexification $E^{(p)}$ is midpoint locally uniformly
convex.
Archive classification: math.FA
Mathematics Subject Classification: 46B20;46B07;46B09
The source file(s), randomized-series2007-01-29.tex: 33940 bytes,
is(are) stored in gzipped form as 0706.3740.gz with size 10kb. The
corresponding postcript file has gzipped size 96kb.
Submitted from: hahnju at postech.ac.kr
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From alspach at www.math.okstate.edu Fri Jul 6 13:47:36 2007
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Date: Fri, 6 Jul 2007 13:47:36 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200707061847.l66IlaLg055672 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Shin-ichi Ohta
Status: R
This is an announcement for the paper "Markov type of Alexandrov
spaces of nonnegative curvature" by Shin-ichi Ohta.
Abstract: We prove that Alexandrov spaces $X$ of nonnegative curvature
have Markov type 2 in the sense of Ball. As a corollary, any Lipschitz
continuous map from a subset of $X$ into a 2-uniformly convex Banach
space is extended as a Lipschitz continuous map on the entire space
$X$.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 46B20, 53C21, 60J10
Remarks: 16 pages
The source file(s), type+.tex: 40468 bytes, is(are) stored in gzipped
form as 0707.0102.gz with size 11kb. The corresponding postcript
file has gzipped size 103kb.
Submitted from: sohta at math.kyoto-u.ac.jp
The paper may be downloaded from the archive by web browser from
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From alspach at www.math.okstate.edu Fri Jul 6 13:48:25 2007
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Date: Fri, 6 Jul 2007 13:48:25 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200707061848.l66ImPB2055702 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Hun Hee Lee
Status: R
This is an announcement for the paper "Tsirelson like operator
spaces" by Hun Hee Lee.
Abstract: We construct nontrivial examples of weak-$C_p$ ($1\leq p
\leq \infty$) operator spaces with the local operator space structure
very close to $C_p = [R, C]_{\frac{1}{p}}$. These examples are
non-homogeneous Hilbertian operator spaces, and their constructions
are similar to that of 2-convexified Tsirelson's space by W. B.
Johnson.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 47L25; 46B07
Remarks: 19 pages
The source file(s), TsirelsonLikeOS.tex: 54208 bytes, is(are) stored
in gzipped form as 0707.0147.gz with size 13kb. The corresponding
postcript file has gzipped size 113kb.
Submitted from: lee.hunhee at gmail.com
The paper may be downloaded from the archive by web browser from
URL
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From alspach at www.math.okstate.edu Fri Jul 6 13:49:08 2007
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Date: Fri, 6 Jul 2007 13:49:08 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200707061849.l66In8UP055732 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Marius Junge and Hun Hee Lee
Status: R
This is an announcement for the paper "A Maurey type result for
operator spaces" by Marius Junge and Hun Hee Lee.
Abstract: The little Grothendieck theorem for Banach spaces says
that every bounded linear operator between $C(K)$ and $\ell_2$ is
2-summing. However, it is shown in \cite{J05} that the operator
space analogue fails. Not every cb-map $v : \K \to OH$ is completely
2-summing. In this paper, we show an operator space analogue of
Maurey's theorem : Every cb-map $v : \K \to OH$ is $(q,cb)$-summing
for any $q>2$ and hence admits a factorization $\|v(x)\| \leq c(q)
\|v\|_{cb} \|axb\|_q$ with $a,b$ in the unit ball of the Schatten
class $S_{2q}$.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 47L25; 46B07
Remarks: 29 pages
The source file(s), MaureyTypeResultOS.tex: 99707 bytes, is(are)
stored in gzipped form as 0707.0152.gz with size 25kb. The corresponding
postcript file has gzipped size 184kb.
Submitted from: lee.hunhee at gmail.com
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URL
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From alspach at www.math.okstate.edu Fri Jul 6 13:50:28 2007
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Date: Fri, 6 Jul 2007 13:50:28 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200707061850.l66IoSkW055778 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Mikael de la Salle
Status: R
This is an announcement for the paper "Equimeasurabily and isometries
in noncommutative Lp-spaces" by Mikael de la Salle.
Abstract: We prove some noncommutative analogues of a theorem by
Rudin and Plotkin about equimeasurability and isometries in L_p-spaces.
Let 0<p<\infty, p not an even integer. The main result of this paper
states that in the category of unital subspaces of noncommutative
probability Lp-spaces, the unital completely isometric maps come
from *-isomorphisms of the underlying von Neumann algebras.
Unfortunately we are only able to treat the case of bounded operators.
Archive classification: math.OA math.FA
Mathematics Subject Classification: 46L53; 46L51; 47L05
Remarks: 11 pages
The source file(s), article_arxiv.bbl: 2056 bytes
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From alspach at www.math.okstate.edu Thu Jul 12 15:51:57 2007
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Date: Thu, 12 Jul 2007 15:51:56 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200707122051.l6CKpuIs099261 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by V.Yaskin
Status: R
This is an announcement for the paper "On strict inclusions in
hierarchies of convex bodies" by V.Yaskin.
Abstract: Let $\mathcal I_k$ be the class of convex $k$-intersection
bodies in $\mathbb{R}^n$ (in the sense of Koldobsky) and $\mathcal
I_k^m$ be the class of convex origin-symmetric bodies all of whose
$m$-dimensional central sections are $k$-intersection bodies. We
show that 1) $\mathcal I_k^m\not\subset \mathcal I_k^{m+1}$, $k+3\le
m<n$, and 2) $\mathcal I_l \not\subset \mathcal I_k$, $1\le k<l <
n-3$.
Archive classification: math.FA
Mathematics Subject Classification: 52A20, 52A21, 46B04
Remarks: 10 pages
The source file(s), Yaskin.tex: 31833 bytes, is(are) stored in
gzipped form as 0707.1471.gz with size 10kb. The corresponding
postcript file has gzipped size 82kb.
Submitted from: vyaskin at math.ou.edu
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URL
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From alspach at www.math.okstate.edu Thu Jul 12 15:52:50 2007
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Date: Thu, 12 Jul 2007 15:52:50 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200707122052.l6CKqoQU099291 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by David Alonso-Gutierrez
Status: R
This is an announcement for the paper "About the isotropy constant
of random convex sets" by David Alonso-Gutierrez.
Abstract: Let $K$ be the symmetric convex hull of $m$ independent
random vectors uniformly distributed on the unit sphere of $\R^n$.
We prove that, for every $\delta>0$, the isotropy constant of $K$
is bounded by a constant $c(\delta)$ with high probability, provided
that $m\geq (1+\delta)n$.
Archive classification: math.FA
Mathematics Subject Classification: 52A20; 52A40; 46B20;
Remarks: 8 pages
The source file(s), Randomconvexsets8.tex: 18946 bytes, is(are)
stored in gzipped form as 0707.1570.gz with size 6kb. The corresponding
postcript file has gzipped size 72kb.
Submitted from: 498220 at celes.unizar.es
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URL
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From banach-bounces at math.okstate.edu Fri Jul 13 08:11:54 2007
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From: Bill Johnson <johnson at math.tamu.edu>
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Subject: [Banach] ANNOUNCEMENT OF SUMIRFAS 2007
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Status: R
ANNOUNCEMENT OF SUMIRFAS 2007
The Informal Regional Functional Analysis Seminar
August 10 - 12
Texas A&M University, College Station
Schedule: Talks for SUMIRFAS will be posted on the Workshop in Analysis and Probability page, URL
http://www.math.tamu.edu/research/workshops/linanalysis/
Below is a list of speakers, current as of July 6. 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 165. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus:
http://www.tamu.edu/map/building/overview/BLOC.html.
Coffee and refreshments will be available in Blocker 155.
The usual SUMIRFAS dinner will be on August 11. It will be a BBQ and swim fest at the home of Jan and Bill Johnson.
Gideon Schechtman, and Joel Zinn, are organizing a Concentration Week on "Probability Inequalities with Applications to High Dimensional Phenomena" that will take place August 6 - August 10. The first day will be devoted to introductory talks designed to introduce non experts to the subject.
We expect to be able to cover housing for most participants from support the
National Science Foundation has provided for the Workshop. Preference will be
given to participants who do not have other sources of support, such as sponsored
research grants. When you ask Cara to book your room, please tell them if
you are requesting support. Minorities, women, graduate students, and young
researchers are especially encouraged to apply.
For logistical support, please contact Cara Barton, cara at math.tamu.edu or Jaime Vykukal, jaime at math.tamu.edu. For more information on the Workshop itself, please contact William Johnson, johnson at math.tamu.edu, David Larson, larson at math.tamu.edu, Gilles Pisier, pisier at math.tamu.edu, or Joel Zinn, jzinn at math.tamu.edu. For
information about the Concentration Week on "Probability Inequalities with Applications to High Dimensional Phenomena", please contact Joel Zinn, jzinn at math.tamu.edu.
SUMIRFAS 2007 Speakers
Grahame Bennett, Series of positive terms
Paco Garcia,
Yehoram Gordon, Best random embedding of $\varepsilon$ nets in convex
bodies, and best random $\varepsilon$ Dvoretzky theorem in the $N-$ dimensional cube
Adrian Ioana, "Cocycle superrigidity for profinite actions of property (T) groups".
Nga Nguyen, Surgery and push-outs on frames
Dmitri Panchenko, "Talagrand's positivity principle"
Marek Ptak,"Hyperreflexivity of finite-dimensional spaces"
Joe Rosenblatt, "Dynamical systems and martingales: the never ending story"
Gideon Schechtman, $\ell_p$ strictly singular operators on $L_p$
Staszek Szarek, "Sets of constant height and applications to quantum information theory"
Piotr Wojdyllo, "Local commutant approach versus Gabor, Wilson, and wavelet tight frames".
Artem Zvavitch, On the local equatorial characterization of zonoids
_______________________________________________
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Banach at math.okstate.edu
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From alspach at www.math.okstate.edu Mon Jul 23 07:43:16 2007
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To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Yongfu Su and Xiaolong Qin
Status: R
This is an announcement for the paper "Strong convergence of modified
Ishikawa iterations for nonlinear mappings" by Yongfu Su and
Xiaolong Qin.
Abstract: In this paper, we prove a strong convergence theorem of
modified Ishikawa iterations for relatively asymptotically nonexpansive
mappings in Banach space. Our results extend and improve the recent
results by Nakajo, Takahashi, Kim, Xu, Matsushita and some others.
Archive classification: math.FA
Mathematics Subject Classification: 47H09, 65J15
Remarks: 11 pages
The source file(s), PM2865new.tex: 31156 bytes
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0707.1955
or
http://arXiv.org/abs/0707.1955
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From alspach at www.math.okstate.edu Mon Jul 23 07:44:24 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200707231244.l6NCiOmX072738 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by T s s R K Rao
Status: R
This is an announcement for the paper "Nice surjections on spaces
of operators" by T s s R K Rao.
Abstract: A bounded linear operator is said to be nice if its adjoint
preserves extreme points of the dual unit ball. Motivated by a
description due to Labuschagne and Mascioni \cite{LM} of such maps
for the space of compact operators on a Hilbert space, in this
article we consider a description of nice surjections on ${\mathcal
K}(X,Y)$ for Banach spaces $X,Y$. We give necessary and sufficient
conditions when nice surjections are given by composition operators.
Our results imply automatic continuity of these maps with respect
to other topologies on spaces of operators. We also formulate the
corresponding result for ${\mathcal L}(X,Y)$ thereby proving an
analogue of the result from \cite{LM} for $L^p$ ($1 <p \neq 2
<\infty$) spaces. We also formulate results when nice operators are
not of the canonical form, extending and correcting the results
from \cite{KS}.
Archive classification: math.FA
Remarks: 8 pages
The source file(s), mat01.cls: 37299 bytes
The paper may be downloaded from the archive by web browser from
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http://front.math.ucdavis.edu/0707.2140
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From alspach at www.math.okstate.edu Mon Jul 23 07:45:44 2007
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Date: Mon, 23 Jul 2007 07:45:44 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200707231245.l6NCjiac072781 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Konrad J Swanepoel
Status: R
This is an announcement for the paper "Extremal problems in Minkowski
space related to minimal networks" by Konrad J Swanepoel.
Abstract: We solve the following problem of Z. F\"uredi, J. C.
Lagarias and F. Morgan [FLM]: Is there an upper bound polynomial
in $n$ for the largest cardinality of a set S of unit vectors in
an n-dimensional Minkowski space (or Banach space) such that the
sum of any subset has norm less than 1? We prove that |S|\leq 2n
and that equality holds iff the space is linearly isometric to
\ell^n_\infty, the space with an n-cube as unit ball. We also remark
on similar questions raised in [FLM] that arose out of the study
of singularities in length-minimizing networks in Minkowski spaces.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 52A40 (Primary) 52A21, 49Q10
(Secondary)
Citation: Proceedings of the American Mathematical Society 124
(1996)
The paper may be downloaded from the archive by web browser from
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http://front.math.ucdavis.edu/0707.3052
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From alspach at www.math.okstate.edu Mon Jul 23 07:46:31 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200707231246.l6NCkVe8072811 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Marco Abate and Jean-Pierre Vigue
Status: R
This is an announcement for the paper "Isometries for the Carathedory
Metric" by Marco Abate and Jean-Pierre Vigue.
Abstract: Under certain hypothesises, we prove that a map which is
an isometry for the Caratheodory infinitesimal metric at a point
is an analytic isomorphism onto its image.
Archive classification: math.FA math.CV
Mathematics Subject Classification: 32H99
Remarks: 6 pages
The source file(s), abate-vigue.tex: 14563 bytes, is(are) stored
in gzipped form as 0707.2329.gz with size 5kb. The corresponding
postcript file has gzipped size 60kb.
Submitted from: vigue at math.univ-poitiers.fr
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From alspach at www.math.okstate.edu Tue Jul 31 11:03:33 2007
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Date: Tue, 31 Jul 2007 11:03:33 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200707311603.l6VG3XmD028670 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by A.Koldobsky, H.Koenig, and M.Zymonopoulou
Status: R
This is an announcement for the paper "The complex Busemann-Petty
problem on sections of convex bodies" by A.Koldobsky, H.Koenig, and
M.Zymonopoulou.
Abstract: The complex Busemann-Petty problem asks whether origin
symmetric convex bodies in $\C^n$ with smaller central hyperplane
sections necessarily have smaller volume. We prove that the answer
is affirmative if $n\le 3$ and negative if $n\ge 4.$
Archive classification: math.FA math.MG
Mathematics Subject Classification: 52A20
Remarks: 18 pages
The source file(s), complexbp.tex: 46749 bytes, is(are) stored in
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postcript file has gzipped size 101kb.
Submitted from: koldobsk at math.missouri.edu
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From alspach at www.math.okstate.edu Tue Jul 31 11:04:51 2007
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Date: Tue, 31 Jul 2007 11:04:50 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200707311604.l6VG4omb028701 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Junsheng Fang, Don Hadwin, Eric Nordgren, and Junhao Shen
Status: R
This is an announcement for the paper "Tracial gauge norms on finite
von Neumann algebras satisfying the weak Dixmier property" by
Junsheng Fang, Don Hadwin, Eric Nordgren, and Junhao Shen.
Abstract: In this paper we set up a representation theorem for
tracial gauge norms on finite von Neumann algebras satisfying the
weak Dixmier property in terms of Ky Fan norms. Examples of tracial
gauge norms on finite von Neumann algebras satisfying the weak
Dixmier property include unitarily invariant norms on finite factors
(type ${\rm II}\sb 1$ factors and $M_n(\cc)$) and symmetric gauge
norms on $L^\infty[0,1]$ and $\cc^n$. As the first application, we
obtain that the class of unitarily invariant norms on a type ${\rm
II}\sb 1$ factor coincides with the class of symmetric gauge norms
on $L^\infty[0,1]$ and von Neumann's classical result~\cite{vN} on
unitarily invariant norms on $M_n(\cc)$. As the second application,
Ky Fan's dominance theorem~\cite{Fan} is obtained for finite von
Neumann algebras satisfying the weak Dixmier property. As the third
application, some classical results in non-commutative $L^p$-theory
(e.g., non-commutative H$\ddot{\text{o}}$lder's inequality, duality
and reflexivity of non-commutative $L^p$-spaces) are obtained for
general unitarily invariant norms on finite factors. We also
investigate the extreme points of $\NN(\M)$, the convex compact set
(in the pointwise weak topology) of normalized unitarily invariant
norms (the norm of the identity operator is 1) on a finite factor
$\M$. We obtain all extreme points of $\NN(M_2(\cc))$ and many
extreme points of $\NN(M_n(\cc))$ ($n\geq 3$). For a type ${\rm
II}\sb 1$ factor $\M$, we prove that if $t$ ($0\leq t\leq 1$) is a
rational number then the Ky Fan $t$-th norm is an extreme point of
$\NN(\M)$.
Archive classification: math.OA math.FA
Mathematics Subject Classification: 46L10, 46L51
Remarks: 56 pages
The source file(s), tracial-gauge-norms.tex: 172272 bytes, is(are)
stored in gzipped form as 0707.4239.gz with size 39kb. The corresponding
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Submitted from: jfang at cisunix.unh.edu
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From alspach at www.math.okstate.edu Tue Jul 31 11:05:53 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200707311605.l6VG5rEm028746 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by M. A. Lopez and S. Reisner
Status: R
This is an announcement for the paper "A note on curves equipartition"
by M. A. Lopez and S. Reisner.
Abstract: The problem of the existence of an equi-partition of a
curve in $\R^n$ has recently been raised in the context of computational
geometry. The problem is to show that for a (continuous) curve
$\Gamma : [0,1] \to \R^n$ and for any positive integer $N$, there
exist points $t_0=0<t_1<...<t_{N-1}<1=t_N$, such that
$d(\Gamma(t_{i-1}),\Gamma(t_i))=d(\Gamma(t_{i}),\Gamma(t_{i+1}))$
for all $i=1,...,N$, where $d$ is a metric or even a semi-metric
(a weaker notion) on $\R^n$. We show here that the existence of
such points, in a much broader context, is a consequence of Brower's
fixed point theorem.
Archive classification: cs.CG math.FA
Mathematics Subject Classification: 58C30; 47H10
The source file(s), equipartition.tex: 10551 bytes, is(are) stored
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Submitted from: reisner at math.haifa.ac.il
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Subject: [Banach] SCHEDULE FOR SUMIRFAS 2007
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Status: R
SCHEDULE FOR SUMIRFAS 2007
The Informal Regional Functional Analysis Seminar
August 10 - 12
Texas A&M University, College Station
Talks for SUMIRFAS will also be posted on the Workshop in Analysis and Probability page:
http://www.math.tamu.edu/research/workshops/linanalysis/
All talks will be in Blocker 165. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus:
http://www.tamu.edu/map/building/overview/BLOC.html
Coffee and refreshments will be available in Blocker 155.
The usual SUMIRFAS dinner will be on August 11. It will be a BBQ at the home of Jan and Bill Johnson.
Gideon Schechtman, and Joel Zinn, are organizing a Concentration Week on "Probability Inequalities with Applications to High Dimensional Phenomena" that will take place August 6 - August 10. The first day will be devoted to introductory talks designed to introduce non experts to the subject.
We expect to be able to cover housing for most participants from support the
National Science Foundation has provided for the Workshop. Preference will be
given to participants who do not have other sources of support, such as sponsored
research grants. When you ask Cara to book your room, please tell them if
you are requesting support. Minorities, women, graduate students, and young
researchers are especially encouraged to apply.
For logistical 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 Larson, larson at math.tamu.edu, Gilles Pisier, pisier at math.tamu.edu, or Joel Zinn, jzinn at math.tamu.edu. For
information about the Concentration Week on "Probability Inequalities with Applications to High Dimensional Phenomena", please contact Joel Zinn, jzinn at math.tamu.edu.
Schedule for SUMIRFAS 2007
Friday, August 10 Blocker 165
1:00- 1:25 Coffee & refreshments, Blocker 155
1:25- 1:30 Greeting
1:30- 2:20 Gideon Schechtman, $\ell_p$ strictly singular operators on $L_p$
2:35- 3:25 Artem Zvavitch, "On the local equatorial characterization of zonoids"
3:30- 4:00 Coffee & refreshments, Blocker 155
4:00- 4:30 Adrian Ioana, "Cocycle superrigidity for profinite actions of property (T) groups"
4:45- 5:35 Marek Ptak,"Hyperreflexivity of finite-dimensional spaces"
Saturday, August 11 Blocker 165
9:00- 9:30 Coffee & refreshments, Blocker 155
9:30-10:20 Joe Rosenblatt, "Dynamical systems and martingales: the never ending story"
10:35-11:05 Paco Garcia, "Superpoligons in Banach spaces"
11:20-11:50 Piotr Wojdyllo, "Local commutant approach versus Gabor, Wilson, and wavelet tight frames"
12:00- 1:45 Lunch
1:45- 2:35 Grahame Bennett, "Series of positive terms"
2:50- 3:40 Staszek Szarek, "Sets of constant height and applications to quantum information theory"
3:45- 4:10 Coffee & refreshments, Blocker 155
4:10- 5:00 Rodrigo Banuelos, "New estimates on the Beurling--Ahlfors operator"
5:15- 5:45 Nga Nguyen, "Surgery and push-outs on frames"
6:45 - BBQ at Jan & Bill Johnson's house, 1306 Deacon Dr., College Station. Please tell Cara, cara at math.tamu.edu, or Jaime, jaime at math.tamu.edu, if you (and spouse or companion, if applicable) will attend.
Sunday, August 12 Blocker 165
9:30-10:00 Coffee & refreshments, Blocker 155
10:00-10:50 Yehoram Gordon, "Best random embedding of $\varepsilon$ nets in convex bodies, and best random $\varepsilon$ Dvoretzky theorem in the $N-$ dimensional cube"
11:05-11:55 Dmitri Panchenko, "Talagrand's positivity principle"
_______________________________________________
Banach mailing list
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From alspach at www.math.okstate.edu Mon Aug 6 11:14:51 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200708061614.l76GEoxJ085570 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Han Ju Lee
Status: R
This is an announcement for the paper "Banach spaces with polynomial
numerical index 1" by Han Ju Lee.
Abstract: We characterize Banach spaces with polynomial numerical
index 1 when they have the Radon-Nikod\'ym property. The holomorphic
numerical index is introduced and the characterization of the Banach
space with holomorphic numerical index 1 is obtained when it has
the Radon-Nikod\'ym property.
Archive classification: math.FA
Mathematics Subject Classification: 46G25; 46B20; 46B22
The source file(s), R070723.tex: 25404 bytes, is(are) stored in
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postcript file has gzipped size 66kb.
Submitted from: hahnju at postech.ac.kr
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From alspach at www.math.okstate.edu Mon Aug 6 11:15:25 2007
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Date: Mon, 6 Aug 2007 11:15:25 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200708061615.l76GFP4o085613 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Han Ju Lee
Status: R
This is an announcement for the paper "Notes on the geometry of
space of polynomials" by Han Ju Lee.
Abstract: We show that the symmetric injective tensor product space
$\hat{\otimes}_{n,s,\varepsilon}E$ is not complex strictly convex
if $E$ is a complex Banach space of $\dim E \ge 2$ and if $n\ge 2$
holds. It is also reproved that $\ell_\infty$ is finitely represented
in $\hat{\otimes}_{n,s,\varepsilon}E$ if $E$ is infinite dimensional
and if $n\ge 2$ holds, which was proved in the other way by Dineen.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
The source file(s), Notes-on-geometry-polynomials-revised.tex: 12189
bytes, is(are) stored in gzipped form as 0708.0331.gz with size
4kb. The corresponding postcript file has gzipped size 53kb.
Submitted from: hahnju at postech.ac.kr
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From alspach at www.math.okstate.edu Mon Aug 6 11:16:40 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200708061616.l76GGeeo085643 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by William B. Johnson and Gideon Schechtman
Status: R
This is an announcement for the paper "Multiplication operators on
$L(L_p)$ and $\ell_p$-strictly singular operators" by William B.
Johnson and Gideon Schechtman.
Abstract: A classification of weakly compact multiplication operators
on $L(L_p)$, $1<p<\infty$, is given. This answers a question raised
by Saksman and Tylli in 1992. The classification involves the concept
of $\ell_p$-strictly singular operators, and we also investigate
the structure of general $\ell_p$-strictly singular operators on
$L_p$. The main result is that if an operator $T$ on $L_p$, $1<p<2$,
is $\ell_p$-strictly singular and $T_{|X}$ is an isomorphism for
some subspace $X$ of $L_p$, then $X$ embeds into $L_r$ for all
$r<2$, but $X$ need not be isomorphic to a Hilbert space.
It is also shown that if $T $ is convolution by a biased coin on
$L_p$ of the Cantor group, $1\le p <2$, and $T_{|X}$ is an isomorphism for some
reflexive subspace $X$ of $L_p$, then $X$ is isomorphic to a Hilbert
space. The case $p=1$ answers a question asked by Rosenthal in 1976.
Archive classification: math.FA
Mathematics Subject Classification: 46B20; 46E30
The source file(s), JSElemOpAug3.07.tex: 53364 bytes, is(are) stored
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Submitted from: gideon at weizmann.ac.il
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From alspach at www.math.okstate.edu Wed Aug 15 10:34:40 2007
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Date: Wed, 15 Aug 2007 10:34:40 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200708151534.l7FFYeXS049692 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Assaf Naor and Yuval Peres
Status: R
This is an announcement for the paper "Embeddings of discrete groups
and the speed of random walks" by Assaf Naor and Yuval Peres.
Abstract: For a finitely generated group G and a banach space X let
\alpha^*_X(G) (respectively \alpha^#_X(G)) be the supremum over all
\alpha\ge 0 such that there exists a Lipschitz mapping (respectively
an equivariant mapping) f:G\to X and c>0 such that for all x,y\in
G we have \|f(x)-f(y)\|\ge c\cdot d_G(x,y)^\alpha. In particular,
the Hilbert compression exponent (respectively the equivariant
Hilbert compression exponent) of G is \alpha^*(G)=\alpha^*_{L_2}(G)
(respectively \alpha^#(G)= \alpha_{L_2}^#(G)). We show that if X
has modulus of smoothness of power type p, then \alpha^#_X(G)\le
\frac{1}{p\beta^*(G)}. Here \beta^*(G) is the largest \beta\ge 0
for which there exists a set of generators S of G and c>0 such that
for all t\in \N we have \E\big[d_G(W_t,e)\big]\ge ct^\beta, where
\{W_t\}_{t=0}^\infty is the canonical simple random walk on the
Cayley graph of G determined by S, starting at the identity element.
This result is sharp when X=L_p, generalizes a theorem of Guentner
and Kaminker and answers a question posed by Tessera. We also show
that if \alpha^*(G)\ge 1/2 then \alpha^*(G\bwr \Z)\ge
\frac{2\alpha^*(G)}{2\alpha^*(G)+1}. This improves the previous
bound due to Stalder and ValetteWe deduce that if we write \Z_{(1)}=
\Z and \Z_{(k+1)}\coloneqq \Z_{(k)}\bwr \Z then
\alpha^*(\Z_{(k)})=\frac{1}{2-2^{1-k}}, and use this result to
answer a question posed by Tessera in on the relation between the
Hilbert compression exponent and the isoperimetric profile of the
balls in G. We also show that the cyclic lamplighter groups C_2\bwr
C_n embed into L_1 with uniformly bounded distortion, answering a
question posed by Lee, Naor and Peres. Finally, we use these results
to show that edge Markov type need not imply Enflo type.
Archive classification: math.MG math.FA math.GR
Remarks: 23 pages
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Submitted from: naor at cims.nyu.edu
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From alspach at www.math.okstate.edu Tue Aug 21 11:02:35 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200708211602.l7LG2ZLX093583 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Ronen Eldan and Boaz Klartag
Status: R
This is an announcement for the paper "Pointwise estimates for
marginals of convex bodies" by Ronen Eldan and Boaz Klartag.
Abstract: We prove a pointwise version of the multi-dimensional
central limit theorem for convex bodies. Namely, let X be an isotropic
random vector in R^n with a log-concave density. For a typical
subspace E in R^n of dimension n^c, consider the probability density
of the projection of X onto E. We show that the ratio between this
probability density and the standard gaussian density in E is very
close to 1 in large parts of E. Here c > 0 is a universal constant.
This complements a recent result by the second named author, where
the total-variation metric between the densities was considered.
Archive classification: math.MG math.FA
Remarks: 17 pages
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postcript file has gzipped size 100kb.
Submitted from: bklartag at princeton.edu
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From alspach at www.math.okstate.edu Fri Aug 24 10:01:43 2007
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Date: Fri, 24 Aug 2007 10:01:43 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200708241501.l7OF1hJe015565 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Horst Martini, Konrad J Swanepoel and Gunter Weiss
Status: R
This is an announcement for the paper "The geometry of Minkowski
spaces --- a survey. Part I" by Horst Martini, Konrad J Swanepoel
and Gunter Weiss.
Abstract: We survey elementary results in Minkowski spaces (i.e.
finite dimensional Banach spaces) that deserve to be collected
together, and give simple proofs for some of them. We place special
emphasis on planar results. Many of these results have often been
rediscovered as lemmas to other results. In Part I we cover the
following topics: The triangle inequality and consequences such as
the monotonicity lemma, geometric characterizations of strict
convexity, normality (Birkhoff orthogonality), conjugate diameters
and Radon curves, equilateral triangles and the affine regular
hexagon construction, equilateral sets, circles: intersection,
circumscribed, characterizations, circumference and area, inscribed
equilateral polygons.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 52A21 (Primary), 46B07, 46B20
(Secondary)
Citation: Expositiones Mathematicae 19 (2001) 97-142
Remarks: 56 pages, 28 figures
The source file(s), fig10.eps: 54544 bytes
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From alspach at www.math.okstate.edu Fri Aug 24 10:02:31 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200708241502.l7OF2V1u015595 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Denny H. Leung and Wee-Kee Tang
Status: R
This is an announcement for the paper "Semilattice structures of
spreading models" by Denny H. Leung and Wee-Kee Tang.
Abstract: Given a Banach space X, denote by SP_{w}(X) the set of
equivalence classes of spreading models of X generated by normalized
weakly null sequences in X. It is known that SP_{w}(X) is a
semilattice, i.e., it is a partially ordered set in which every
pair of elements has a least upper bound. We show that every countable
semilattice that does not contain an infinite increasing sequence
is order isomorphic to SP_{w}(X) for some separable Banach space
X.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B15
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bytes, is(are) stored in gzipped form as 0708.3126.gz with size
11kb. The corresponding postcript file has gzipped size 92kb.
Submitted from: weekee.tang at nie.edu.sg
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From alspach at www.math.okstate.edu Tue Aug 28 19:32:22 2007
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Date: Tue, 28 Aug 2007 19:32:22 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200708290032.l7T0WM0C058546 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Gilles Pisier
Status: R
This is an announcement for the paper "A remark on hypercontractive
semigroups and operator ideals" by Gilles Pisier.
Abstract: In this note, we answer a question raised by Johnson and
Schechtman \cite{JS}, about the hypercontractive semigroup on
$\{-1,1\}^{\NN}$. More generally, we prove the folllowing theorem.
Let $1<p<2$. Let $(T(t))_{t>0}$ be a holomorphic semigroup on $L_p$
(relative to a probability space). Assume the following mild form
of hypercontractivity: for some large enough number $s>0$, $T(s)$
is bounded from $L_p$ to $L_2$. Then for any $t>0$, $T(t)$ is in
the norm closure in $B(L_p)$ (denoted by $\overline{\Gamma_2}$) of
the subset (denoted by ${\Gamma_2}$) formed by the operators mapping
$L_p$ to $L_2$ (a fortiori these operators factor through a Hilbert
space).
Archive classification: math.FA
Mathematics Subject Classification: 47D06
The source file(s), hyper.tex: 11355 bytes, is(are) stored in gzipped
form as 0708.3423.gz with size 5kb. The corresponding postcript
file has gzipped size 50kb.
Submitted from: gip at ccr.jussieu.fr
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From alspach at www.math.okstate.edu Fri Aug 31 07:24:47 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200708311224.l7VCOll0077714 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by N.J. Kalton and G. Lancien
Status: R
This is an announcement for the paper "Best constants for Lipschitz
embeddings of metric spaces into $c_0$" by N.J. Kalton and G.
Lancien.
Abstract: We answer a question of Aharoni by showing that every
separable metric space can be Lipschitz 2-embedded into $c_0$ and
this result is sharp; this improves earlier estimates of Aharoni,
Assouad and Pelant. We use our methods to examine the best constant
for Lipschitz embeddings of the classical $\ell_p-$spaces into $c_0$
and give other applications. We prove that if a Banach space embeds
almost isometrically into $c_0$, then it embeds linearly almost
isometrically into $c_0$. We also study Lipschitz embeddings into
$c_0^+$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20; 46T99
Remarks: 22 pages
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Submitted from: gilles.lancien at univ-fcomte.fr
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From alspach at www.math.okstate.edu Fri Aug 31 07:25:28 2007
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Date: Fri, 31 Aug 2007 07:25:28 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200708311225.l7VCPSjw077755 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Yun Sung Choi Kwang Hee Han Han Ju Lee
Status: R
This is an announcement for the paper "Boundaries for algebras of
holomorphic functions on Banach spaces" by Yun Sung Choi Kwang Hee
Han Han Ju Lee.
Abstract: We study the relations between boundaries for algebras
of holomorphic functions on Banach spaces and complex convexity of
their balls. In addition, we show that the Shilov boundary for
algebras of holomorphic functions on an order continuous sequence
space $X$ is the unit sphere $S_X$ if $X$ is locally c-convex. In
particular, it is shown that the unit sphere of the Orlicz-Lorentz
sequence space $\lambda_{\varphi, w}$ is the Shilov boundary for
algebras of holomorphic functions on $\lambda_{\varphi, w}$ if
$\varphi$ satisfies the $\delta_2$-condition.
Archive classification: math.FA
Mathematics Subject Classification: 46E50; 46B20; 46B45
The source file(s), shilovboundary-final-corrected.tex: 39013 bytes,
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corresponding postcript file has gzipped size 102kb.
Submitted from: hahnju at postech.ac.kr
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From alspach at www.math.okstate.edu Fri Aug 31 07:26:40 2007
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Date: Fri, 31 Aug 2007 07:26:39 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200708311226.l7VCQdPv077785 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Yun Sung Choi, Han Ju Lee, and Hyun Gwi Song
Status: R
This is an announcement for the paper "Bishop's theorem and
differentiability of a subspace of $C_b(K)$" by Yun Sung Choi, Han
Ju Lee, and Hyun Gwi Song.
Abstract: Let $K$ be a Hausdorff space and $C_b(K)$ be the Banach
algebra of all complex bounded continuous functions on $K$. We study
the G\^{a}teaux and Fr\'echet differentiability of subspaces of
$C_b(K)$. Using this, we show that the set of all strong peak
functions in a nontrivial separating separable subspace $H$ of
$C_b(K)$ is a dense $G_\delta$ subset of $H$, if $K$ is compact.
This gives a generalized Bishop's theorem, which says that the
closure of the set of strong peak point for $H$ is the smallest
closed norming subset of $H$. The classical Bishop's theorem was
proved for a separating subalgebra $H$ and a metrizable compact
space $K$.
In the case that $X$ is a complex Banach space with the Radon-Nikod\'ym
property, we show that the set of all strong peak functions in
$A_b(B_X)=\{ f\in C_b(B_X) : f|_{B_X^\circ} \mbox{ is holomorphic}\}$
is dense. As an application, we show that the smallest closed norming
subset of $A_b(B_X)$ is the closure of the set of all strong peak
points for $A_b(B_X)$. This implies that the norm of $A_b(B_X)$ is
G\^{a}teaux differentiable on a dense subset of $A_b(B_X)$, even
though the norm is nowhere Fr\'echet differentiable when $X$ is
nontrivial. We also study the denseness of norm attaining holomorphic
functions and polynomials. Finally we investigate the existence of
numerical Shilov boundary.
Archive classification: math.FA
Mathematics Subject Classification: 46B04; 46G20; 46G25; 46B22
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From alspach at www.math.okstate.edu Wed Sep 5 08:13:33 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200709051313.l85DDXOJ010732 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Marius Junge and Quanhua Xu
Status: R
This is an announcement for the paper "Counterexamples for the
convexity of certain matricial inequalities" by Marius Junge and
Quanhua Xu.
Abstract: In \cite{CL} Carlen and Lieb considered Minkowski type
inequalities in the context of operators on a Hilbert space. More
precisely, they considered the homogenous expression
\[ f_{pq}(x_1,...,x_n) \lel \big(tr\big((\sum_{k=1}^n
x_k^q)^{p/q}\big)\big)^{1/p} \pl \] defined for positive matrices.
The concavity for $q=1$ and $p<1$ yields
strong subadditivity for quantum entropy. We discuss the convexity
of $f_{pq}$ and show that, contrary to the commutative case, there
exists a $q_0>1$ such that $f_{1q}$ is not convex for all $1<q<q_0$.
This is achieved by constructing a family of interesting channels
on $2\times 2$ matrices.
Archive classification: math.FA math-ph math.MP
Mathematics Subject Classification: 46L25 15A48
The source file(s), cedriv.tex: 58533 bytes, is(are) stored in
gzipped form as 0709.0433.gz with size 18kb. The corresponding
postcript file has gzipped size 129kb.
Submitted from: junge at math.uiuc.edu
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From alspach at www.math.okstate.edu Wed Sep 5 08:17:30 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200709051317.l85DHUug010777 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Joel A. Tropp
Status: R
This is an announcement for the paper "On the linear independence
of spikes and sines" by Joel A. Tropp.
Abstract: The purpose of this work is to survey what is known about
the linear independence of spikes and sines. The paper provides new
results for the case where the locations of the spikes and the
frequencies of the sines are chosen at random. This problem is
equivalent to studying the spectral norm of a random submatrix drawn
from the discrete Fourier transform matrix. The proof involves
methods from geometric functional analysis.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B07, 47A11, 15A52
Remarks: 4 figures
The source file(s), art/old/square-unnorm.eps: 11263 bytes, etc.,
is(are) stored in gzipped form as 0709.0517.tar.gz with size 344kb.
The corresponding postcript file has gzipped size 173kb.
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From alspach at www.math.okstate.edu Mon Sep 10 14:02:38 2007
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Message-Id: <200709101902.l8AJ2c4c045694 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Sorina Barza, Viktor Kolyada, and Javier Soria
Status: R
This is an announcement for the paper "Sharp constants related to
the triangle inequality in Lorentz spaces" by Sorina Barza, Viktor
Kolyada, and Javier Soria.
Abstract: We study the Lorentz spaces $L^{p,s}(R,\mu)$ in the range
$1<p<s\le \infty$, for which the standard functional $$
||f||_{p,s}=\left(\int_0^\infty (t^{1/p}f^*(t))^s\frac{dt}{t}\right)^{1/s}
$$ is only a quasi-norm. We find the optimal constant in the
triangle inequality
for this quasi-norm, which leads us to consider the following
decomposition norm:
$$ ||f||_{(p,s)}=\inf\bigg\{\sum_{k}||f_k||_{p,s}\bigg\}, $$ where
the infimum is taken over all finite representations $f=\sum_{k}f_k.
$ We also prove that the decomposition norm and the dual norm $$
||f||_{p,s}'= \sup\left\{ \int_R fg\,d\mu: ||g||_{p',s'}=1\right\}
$$ agree for all values $p,s>1$.
Archive classification: math.FA math.CA
Mathematics Subject Classification: 46E30, 46B25
Remarks: 24 pages
The source file(s), Norms-Constants.tex: 47398 bytes
The paper may be downloaded from the archive by web browser from
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From alspach at www.math.okstate.edu Mon Sep 10 14:03:50 2007
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Date: Mon, 10 Sep 2007 14:03:50 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200709101903.l8AJ3oiC045725 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Osman Gueler and Filiz Guertuna
Status: R
This is an announcement for the paper "The extremal volume ellipsoids
of convex bodies, their symmetry properties, and their determination
in some special cases" by Osman Gueler and Filiz Guertuna.
Abstract: A convex body K has associated with it a unique circumscribed
ellipsoid CE(K) with minimum volume, and a unique inscribed ellipsoid
IE(K) with maximum volume. We first give a unified, modern exposition
of the basic theory of these extremal ellipsoids using the semi-infinite
programming approach pioneered by Fritz John in his seminal 1948
paper. We then investigate the automorphism groups of convex bodies
and their extremal ellipsoids. We show that if the automorphism
group of a convex body K is large enough, then it is possible to
determine the extremal ellipsoids CE(K) and IE(K) exactly, using
either semi-infinite programming or nonlinear programming. As
examples, we compute the extremal ellipsoids when the convex body
K is the part of a given ellipsoid between two parallel hyperplanes,
and when K is a truncated second order cone or an ellipsoidal
cylinder.
Archive classification: math.OC math.FA
Mathematics Subject Classification: 90C34; 46B20; 90C30; 90C46;
65K10
Remarks: 36 pages
The source file(s), Ellipsoid35.bbl: 8177 bytes
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0709.0707
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http://arXiv.org/abs/0709.0707
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From alspach at www.math.okstate.edu Thu Sep 13 14:40:42 2007
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Date: Thu, 13 Sep 2007 14:40:42 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200709131940.l8DJegfF066821 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Tuomas Hytonen, Jan van Neerven, and Pierre Portal
Status: R
This is an announcement for the paper "Conical square functions in
UMD Banach spaces" by Tuomas Hytonen, Jan van Neerven, and Pierre
Portal.
Abstract: We study conical square function estimates for Banach-valued
functions, and introduce a vector-valued analogue of the
Coifman-Meyer-Stein tent spaces. Following recent work of
Auscher-McIntosh-Russ, the tent spaces in turn are used to construct
a scale of vector-valued Hardy spaces associated with a given
bisectorial operator \(A\) with certain off-diagonal bounds, such
that \(A\) always has a bounded \(H^{\infty}\)-functional calculus
on these spaces. This provides a new way of proving functional
calculus of \(A\) on the Bochner spaces \(L^p(\R^n;X)\) by checking
appropriate conical square function estimates, and also a conical
analogue of Bourgain's extension of the Littlewood-Paley theory to
the UMD-valued context. Even when \(X=\C\), our approach gives
refined \(p\)-dependent versions of known results.
Archive classification: math.FA math.SP
Mathematics Subject Classification: Primary: 46B09; Secondary:
42B25, 42B35, 46B09, 46E40, 47A60, 47F05
Remarks: 28 pages; submitted for publication
The source file(s), tent/newsymbol.sty: 440 bytes tent/tent.bbl:
5616 bytes tent/tent.tex: 91867 bytes, is(are) stored in gzipped
form as 0709.1350.tar.gz with size 29kb. The corresponding postcript
file has gzipped size 167kb.
Submitted from: J.M.A.M.vanNeerven at tudelft.nl
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URL
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From alspach at www.math.okstate.edu Fri Sep 28 09:44:44 2007
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Date: Fri, 28 Sep 2007 09:44:44 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200709281444.l8SEiimd017152 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by R. M. Dudley, Sergiy Sidenko, Zuoqin Wang, and Fangyun Yang
Status: R
This is an announcement for the paper "Some classes of rational
functions and related Banach spaces" by R. M. Dudley, Sergiy Sidenko,
Zuoqin Wang, and Fangyun Yang.
Abstract: For positive integers d, r, and M, we consider the class
of rational functions on real d-dimensional space whose denominators
are products of at most r functions of the form 1+Q(x) where each
Q is a quadratic form with eigenvalues bounded above by M and below
by 1/M. Each numerator is a monic monomial of the same degree as
the corresponding denominator. Then we form the Banach space of
countable linear combinations of such rational functions with
absolutely summable coefficients, normed by the infimum of sums of
absolute values of the coefficients. We show that for rational
functions whose denominators are rth powers of a specific 1+Q, or
differences of two such rational functions with the same numerator,
the norm is achieved by and only by the obvious combination of one
or two functions respectively. We also find bounds for coefficients
in partial-fraction decompositions of some specific rational
functions, which in some cases are quite sharp.
Archive classification: math.FA
Mathematics Subject Classification: 46B99 (primary), 46B22 (secondary)
Remarks: LaTex, 18 pages, no figures
The source file(s), bspsrtlfncts.tex: 74856 bytes, is(are) stored
in gzipped form as 0709.2449.gz with size 25kb. The corresponding
postcript file has gzipped size 93kb.
Submitted from: rmd at math.mit.edu
The paper may be downloaded from the archive by web browser from
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http://front.math.ucdavis.edu/0709.2449
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From alspach at www.math.okstate.edu Fri Sep 28 09:45:28 2007
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Date: Fri, 28 Sep 2007 09:45:27 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200709281445.l8SEjRN1017193 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Anna Maria Pelczar
Status: R
This is an announcement for the paper "Note on distortion and
Bourgain $\ell_1$ index" by Anna Maria Pelczar.
Abstract: The relation between different notions measuring proximity
to $\ell_1$ and distortability of a Banach space is studied. The
main result states that a Banach space, whose all subspaces have
Bourgain $\ell_1$ index greater than $\omega^\alpha$, $\alpha<\omega_1$,
contains either an arbitrary distortable subspace or an
$\ell_1^\alpha$-asymptotic subspace.
Archive classification: math.FA
Mathematics Subject Classification: 46B20 (primary), 46B03 (secondary)
Remarks: 10 pages
The source file(s), distortion_bourgain.tex: 36771 bytes, is(are)
stored in gzipped form as 0709.2272.gz with size 11kb. The corresponding
postcript file has gzipped size 92kb.
Submitted from: anna.pelczar at im.uj.edu.pl
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URL
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From alspach at www.math.okstate.edu Fri Sep 28 09:46:21 2007
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Date: Fri, 28 Sep 2007 09:46:21 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200709281446.l8SEkL51017225 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Dongni Tan
Status: R
This is an announcement for the paper "On maps which preserve
equality of distance in F-spaces" by Dongni Tan.
Abstract: In order to generalize the results of Mazur-Ulam and Vogt,
we shall prove that any map T which preserves equality of distance
with T(0)=0 between two F-spaces without surjective condition is
linear. Then , as a special case linear isometries are characterized
through a simple property of their range.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46A16
Remarks: 11 pages, 385 figures
The source file(s), DongniTan.tex: 17852 bytes, is(are) stored in
gzipped form as 0709.3620.gz with size 6kb. The corresponding
postcript file has gzipped size 66kb.
Submitted from: 0110127 at mail.nankai.edu.cn
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URL
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From banach-bounces at math.okstate.edu Thu Oct 11 07:19:14 2007
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Subject: [Banach] Kent State Informal Analysis Seminar October 27-28
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Status: R
Dear Friends,
In October 27-28, 2007 (Saturday-Sunday), the Department of
Mathematical Science at Kent State University will run the famous but
still very informal
INFORMAL ANALYSIS SEMINAR
The plan for now is to start in the morning of Saturday October 27
and finish around 3-4pm Sunday October 28 (this time it was decided
to not have a break for Saturday night, it will save us and you
some hotel money :) ). The list of speakers will include
* Keith Ball (University College London).
* Alexandre Eremenko (Purdue University).
* William B. Johnson (Texas A&M University).
* Fedor Nazarov (University of Wisconsin-Madison).
* Andreas Seeger (University of Wisconsin-Madison).
* Thomas Schlumprecht(Texas A&M University).
* Vladimir Temlyakov (University of South Carolina)
It would be great if you could visit Kent State and participate in the
seminar! May we ask you to respond as soon as possible, so that we can
gauge the need for housing, lecture room(s), etc.
Please, check
http://www.math.kent.edu/math/Informal-Analysis-Seminar-2007.cfm
for more information.
The Seminar is supported by the Department of Mathematical Sciences and
NSF Focused Research Group: Fourier analytic and probabilistic methods
in geometric functional analysis and convexity. Minorities, women,
graduate students, and young researchers are especially encouraged to
attend.
Best Regards,
Analysis group at Kent State!
_______________________________________________
Banach mailing list
Banach at math.okstate.edu
http://mail.math.okstate.edu/mailman/listinfo/banach
From alspach at www.math.okstate.edu Sun Oct 14 09:26:44 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
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To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Gitta Kutyniok, Ali Pezeshki, Robert Calderbank, and Taotao Liu
Status: R
This is an announcement for the paper "Robust dimension reduction,
fusion frames, and Grassmannian packings" by Gitta Kutyniok, Ali
Pezeshki, Robert Calderbank, and Taotao Liu.
Abstract: We consider estimating a random vector from its noisy
projections onto low dimensional subspaces constituting a fusion
frame. A fusion frame is a collection of subspaces, for which the
sum of the projection operators onto the subspaces is bounded below
and above by constant multiples of the identity operator. We first
determine the minimum mean-squared error (MSE) in linearly estimating
the random vector of interest from its fusion frame projections,
in the presence of white noise. We show that MSE assumes its minimum
value when the fusion frame is tight. We then analyze the robustness
of the constructed linear minimum MSE (LMMSE) estimator to erasures
of the fusion frame subspaces. We prove that tight fusion frames
consisting of equi-dimensional subspaces have maximum robustness
(in the MSE sense) with respect to erasures of one subspace, and
that the optimal subspace dimension depends on signal-to-noise ratio
(SNR). We also prove that tight fusion frames consisting of
equi-dimensional subspaces with equal pairwise chordal distances
are most robust with respect to two and more subspace erasures. We
call such fusion frames equi-distance tight fusion frames, and prove
that the chordal distance between subspaces in such fusion frames
meets the so-called simplex bound, and thereby establish connections
between equi-distance tight fusion frames and optimal Grassmannian
packings. Finally, we present several examples for construction
of equi-distance tight fusion frames.
Archive classification: math.FA
Mathematics Subject Classification: 94A12; 42C15; 68P30; 93E10
Remarks: 21 pages
The source file(s), fusionframe_final_arxiv.bbl: 2844 bytes
The paper may be downloaded from the archive by web browser from
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From alspach at www.math.okstate.edu Sun Oct 14 09:28:13 2007
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Date: Sun, 14 Oct 2007 09:28:13 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200710141428.l9EESDWQ020791 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Chang-Pao Chen, Chun-Yen Shen, and Kuo-Zhong Wang
Status: R
This is an announcement for the paper "Characterization of the
matrix whose norm is determined by its action on decreasing sequences:
The exceptional cases" by Chang-Pao Chen, Chun-Yen Shen, and Kuo-Zhong
Wang.
Abstract: Let $A=(a_{j,k})_{j,k \ge 1}$ be a non-negative matrix.
In this paper, we characterize those $A$ for which $\|A\|_{\ell_p,\ell_q}$
are determined by their actions on non-negative decreasing sequences,
where one of $p$ and $q$ is 1 or $\infty$. The conditions forcing
on $A$ are sufficient and they are also necessary for non-negative
finite matrices.
Archive classification: math.FA math.CA
Mathematics Subject Classification: 15A60, 47A30, 47B37
The source file(s), shenwang9409016.tex: 25759 bytes, is(are) stored
in gzipped form as 0710.0038.gz with size 8kb. The corresponding
postcript file has gzipped size 79kb.
Submitted from: shenc at indiana.edu
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From alspach at www.math.okstate.edu Sun Oct 14 09:29:02 2007
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Date: Sun, 14 Oct 2007 09:29:02 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200710141429.l9EET2Ft020821 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Dominique Lecomte
Status: R
This is an announcement for the paper "How can we recover Baire
class one functions?" by Dominique Lecomte.
Abstract: Let X and Y be separable metrizable spaces, and f:X-->Y
be a function. We want to recover f from its values on a small set
via a simple algorithm. We show that this is possible if f is Baire
class one, and in fact we get a characterization. This leads us to
the study of sets of Baire class one functions and to a characterization
of the separability of the dual space of an arbitrary Banach space.
Archive classification: math.LO math.FA math.GN
Mathematics Subject Classification: 2000 MSC 26A21, 54H05, 03E15,
46A20
Citation: Mathematika 50 (2003) 171-198
The source file(s), 06.HcrB1f.tex: 108181 bytes, is(are) stored in
gzipped form as 0710.0155.gz with size 29kb. The corresponding
postcript file has gzipped size 132kb.
Submitted from: lecomte at moka.ccr.jussieu.fr
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Date: Sun, 14 Oct 2007 09:30:12 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200710141430.l9EEUCFB020861 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Stanislaw J. Szarek, Elisabeth Werner and Karol Zyczkowski
Status: R
This is an announcement for the paper "Geometry of sets of quantum
maps: a generic positive map acting on a high-dimensional system
is not completely positive" by Stanislaw J. Szarek, Elisabeth Werner
and Karol Zyczkowski.
Abstract: We investigate the set a) of positive, trace preserving
maps acting on density matrices of size N, and a sequence of its
nested subsets: the sets of maps which are b) decomposable, c)
completely positive, d) extended by identity impose positive partial
transpose and e) are superpositive. Working with the Hilbert-Schmidt
(Euclidean) measure we derive tight explicit two-sided bounds for
the volumes of all five sets. A sample consequence is the fact that,
as N increases, a generic positive map becomes not decomposable
and, a fortiori, not completely positive.
Due to the Jamiolkowski isomorphism, the results obtained for
quantum maps are closely connected to similar relations between the volume of
the set of quantum states and the volumes of its subsets (such as
states with positive partial transpose or separable states) or
supersets. Our approach depends on systematic use of duality to
derive quantitative estimates, and on various tools of classical
convexity, high-dimensional probability and geometry of Banach
spaces, some of which are not standard.
Archive classification: quant-ph math.FA
Remarks: 34 pages in Latex including 3 figures in eps
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. The corresponding postcript file has gzipped size .
Submitted from: karol at tatry.if.uj.edu.pl
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From alspach at www.math.okstate.edu Sun Oct 14 09:31:04 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200710141431.l9EEV4g1020892 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by H.H. Bauschke, F. Deutsch and H. Hundal
Status: R
This is an announcement for the paper "Characterizing arbitrarily
slow convergence in the method of alternating projections" by
H.H. Bauschke, F. Deutsch and H. Hundal.
Abstract: In 1997, Bauschke, Borwein, and Lewis have stated a
trichotomy theorem that characterizes when the convergence of the
method of alternating projections can be arbitrarily slow. However,
there are two errors in their proof of this theorem. In this note,
we show that although one of the errors is critical, the theorem
itself is correct. We give a different proof that uses the
multiplicative form of the spectral theorem, and the theorem holds
in any real or complex Hilbert space, not just in a real Hilbert
space.
Archive classification: math.FA math.OC
Mathematics Subject Classification: 47B20
The source file(s), 071010.tex: 35102 bytes, is(are) stored in
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postcript file has gzipped size 96kb.
Submitted from: heinz.bauschke at ubc.ca
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>From banach-bounces at math.okstate.edu Fri Oct 12 12:35:35 2007
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Date: Thu, 11 Oct 2007 21:48:59 -0600
From: Nicole Tomczak-Jaegermann <nicole at ellpspace.math.ualberta.ca>
Message-ID: <20071012034859.GA12893 at ellpspace.math.ualberta.ca>
Subject: [Banach] position in Geometric Functional Analysis at Alberta
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Tenure Track Position, Geometrical Functional Analysis
The Department of Mathematical and Statistical Sciences at the University
of Alberta invites applications for a tenure track position in the area of
Geometrical Functional Analysis. We primarily seek candidates at the
Assistant Professor level, but exceptional candidates at a more senior
level will be considered.
The successful candidate will have established accomplishments and
outstanding promise in research, as well as a strong commitment to
graduate and undergraduate teaching. Candidates must hold a PhD
degree. We offer an excellent research environment with a normal
teaching load of three courses per year. A fit with some of the
existing research being presently conducted in the Department is an
asset. For more information about the Department, please visit our
website at http://www.math.ualberta.ca/.
We are looking for specialists in any of the areas of geometric functional
analysis including asymptotic theory of normed spaces and high-dimensional
convex geometry, related probabilistic methods, geometric inequalities and
concentration inequalities, and related discrete mathematics aspects.
Current research strengths in the analysis group of the Department include
asymptotic geometric analysis, abstract harmonic analysis, Banach spaces,
Banach algebras and Banach lattices, operator theory, approximation
theory, Fourier and wavelet analysis.
Alberta is one of the leading Mathematics Departments in Canada and has
strong connections with other mathematical institutes, such as the Pacific
Institute for the Mathematical Sciences (PIMS), Mathematics of Information
Technology and Complex Systems (MITACS), and the Banff International
Research Station (BIRS).
Applications should include a curriculum vitae, a research statement, a
teaching profile outlining experience and/or interests, and at least three
confidential letters of reference.
The closing date for applications is November 16, 2007, or until a
suitable candidate is found. Early applications are encouraged.
Interested applicants may apply to:
Arturo Pianzola, Chair
Department of Mathematical and Statistical Sciences
University of Alberta
Edmonton, Alberta, Canada T6G 2G1
Email: chairsec at math.ualberta.ca
All qualified candidates are encouraged to apply; however, Canadians and
permanent residents will be given priority. If suitable Canadian citizens
or permanent residents cannot be found, other individuals will be
considered.
The University of Alberta hires on the basis of merit. We are committed to
the principle of equity in employment. We welcome diversity and encourage
applications from all qualified women and men, including persons with
disabilities, members of visible minorities, and Aboriginal persons.
_______________________________________________
Banach mailing list
Banach at math.okstate.edu
http://mail.math.okstate.edu/mailman/listinfo/banach
From alspach at www.math.okstate.edu Mon Oct 29 08:06:53 2007
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Date: Mon, 29 Oct 2007 08:06:53 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200710291306.l9TD6rvT024620 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jan van Neerven
Status: R
This is an announcement for the paper "Compactness in vector-valued
Banach function spaces" by Jan van Neerven.
Abstract: We give a new proof of a recent characterization by Diaz
and Mayoral of compactness in the Lebesgue-Bochner spaces $L_X^p$,
where $X$ is a Banach space and $1\le p<\infty$, and extend the
result to vector-valued Banach function spaces $E_X$, where $E$ is
a Banach function space with order continuous norm.
Archive classification: math.FA
Mathematics Subject Classification: 46E40
Citation: Positivity 11 (2007), 461-467
Remarks: 6 pages
The source file(s), compact_BFS.tex: 39718 bytes, is(are) stored
in gzipped form as 0710.3241.gz with size 13kb. The corresponding
postcript file has gzipped size 68kb.
Submitted from: J.M.A.M.vanNeerven at tudelft.nl
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From alspach at www.math.okstate.edu Mon Oct 29 08:07:30 2007
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Date: Mon, 29 Oct 2007 08:07:30 -0500 (CDT)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200710291307.l9TD7UYq024650 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Richard J. Smith
Status: R
This is an announcement for the paper "Trees, linear orders and
G\^ateaux smooth norms" by Richard J. Smith.
Abstract: We introduce a linearly ordered set Z and use it to prove
a necessity condition for the existence of a G\^ateaux smooth norm
on C(T), where T is a tree. This criterion is directly analogous
to the corresponding equivalent condition for Fr\'echet smooth
norms. In addition, we prove that if C(T) admits a G\^ateaux smooth
lattice norm then it also admits a lattice norm with strictly convex
dual norm.
Archive classification: math.FA
Mathematics Subject Classification: 46B03; 46B26
Remarks: A different version of this paper is to appear in J. London
Math. Soc
The source file(s), arxiv12-10-07.tex: 60917 bytes, is(are) stored
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Submitted from: rjs209 at cam.ac.uk
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From alspach at www.math.okstate.edu Sun Nov 4 08:05:40 2007
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Date: Sun, 4 Nov 2007 08:05:39 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200711041405.lA4E5dXE073661 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Richard J. Smith
Status: R
This is an announcement for the paper "Gruenhage compacta and
strictly convex dual norms" by Richard J. Smith.
Abstract: We prove that if K is a Gruenhage compact space then C(K)*
admits an equivalent, strictly convex dual norm. As a corollary,
we show that if X is a Banach space and X* is the |.|-closed linear
span of K, where K is a Gruenhage compact in the w*-topology and
|.| is equivalent to a coarser, w*-lower semicontinuous norm on X*,
then X* admits an equivalent, strictly convex dual norm. We give a
partial converse to the first result by showing that if T is a tree,
then C(T)* admits an equivalent, strictly convex dual norm if and
only if T is a Gruenhage space. Finally, we present some stability
properties satisfied by Gruenhage spaces; in particular, Gruenhage
spaces are stable under perfect images.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 46B03; 46B26
The source file(s), arxiv29-10-07.tex: 67073 bytes, is(are) stored
in gzipped form as 0710.5396.gz with size 19kb. The corresponding
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Submitted from: rjs209 at cam.ac.uk
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From alspach at www.math.okstate.edu Sun Nov 4 08:06:30 2007
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(envelope-from alspach)
Date: Sun, 4 Nov 2007 08:06:30 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200711041406.lA4E6Un8073692 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by David Alonso-Gutierrez
Status: R
This is an announcement for the paper "On an extension of the
Blaschke-Santalo inequality" by David Alonso-Gutierrez.
Abstract: Let $K$ be a convex body and $K^\circ$ its polar body.
Call $\phi(K)=\frac{1}{|K||K^\circ|}\int_K\int_{K^\circ}\langle
x,y\rangle^2 dxdy$. It is conjectured that $\phi(K)$ is maximum
when $K$ is the euclidean ball. In particular this statement implies
the Blaschke-Santalo inequality. We verify this conjecture when $K$
is restricted to be a $p$--ball.
Archive classification: math.FA
Mathematics Subject Classification: 52A20; 52A40; 46B20
Remarks: 7 pages
The source file(s), p-balls5.tex: 18249 bytes, is(are) stored in
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Submitted from: 498220 at celes.unizar.es
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From alspach at www.math.okstate.edu Sun Nov 4 08:07:37 2007
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Date: Sun, 4 Nov 2007 08:07:37 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200711041407.lA4E7bRQ073722 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Haskell P. Rosenthal
Status: R
This is an announcement for the paper "Some new characterizations
of Banach spaces containing $\ell^1$" by Haskell P. Rosenthal.
Abstract: Several new characterizations of Banach spaces containing
a subspace isomorphic to $\ell^1$, are obtained. These are applied
to the question of when $\ell^1$ embeds in the injective tensor
product of two Banach spaces.
Archive classification: math.FA
Remarks: 27 pages, AMSLaTeX
The source file(s), new-char.tex: 120502 bytes, is(are) stored in
gzipped form as 0710.5944.gz with size 35kb. The corresponding
postcript file has gzipped size 163kb.
Submitted from: combs at mail.ma.utexas.edu
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From alspach at www.math.okstate.edu Mon Nov 12 21:59:50 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
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To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Hun Hee Lee
Status: RO
This is an announcement for the paper "Finite dimensional subspaces
of noncommutative $L_p$ spaces" by Hun Hee Lee.
Abstract: We prove the following noncommutative version of Lewis's
classical result. Every n-dimensional subspace E of Lp(M) (1<p<\infty)
for a von Neumann algebra M satisfies d_{cb}(E, RC^n_{p'}) \leq c_p
n^{\abs{1/2-1/p}} for some constant c_p depending only on $p$, where
$1/p +1/p' =1$ and $RC^n_{p'} = [R_n\cap C_n, R_n+C_n]_{1/p'}$.
Moreover, there is a projection $P:Lp(M) --> Lp(M)$ onto E with
$\norm{P}_{cb} \leq c_p n^{\abs{1/2-1/p}}.$ We follow the classical
change of density argument with appropriate noncommutative variations
in addition to the opposite trick.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 47L25; 46B07
Remarks: 15 pages
The source file(s), FD-NoncomLp-Update.tex: 51003 bytes, is(are)
stored in gzipped form as 0711.1208.gz with size 14kb. The corresponding
postcript file has gzipped size 109kb.
Submitted from: lee.hunhee at gmail.com
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From alspach at www.math.okstate.edu Tue Nov 13 10:36:56 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200711131636.lADGau0j036708 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Valentin Ferenczi and Christian Rosendal
Status: R
This is an announcement for the paper "Banach spaces without minimal
subspaces" by Valentin Ferenczi and Christian Rosendal.
Abstract: We prove three new dichotomies for Banach spaces \`a la
W. T. Gowers' dichotomies. The three dichotomies characterise
respectively the spaces having no minimal subspaces, having no
subsequentially minimal basic sequences, and having no subspaces
crudely finitely representable in all of their subspaces. We
subsequently use these results to make progress on the program of
Gowers of classifying Banach spaces by finding characteristic spaces
present in every space. Also, the results are used to embed any
partial order of size $\aleph_1$ into the subspaces of any space
without a minimal subspace ordered by isomorphic embeddability.
Finally, we analyse several examples of spaces and classify them
according to which side of the dichotomies they fall.
Archive classification: math.FA math.LO
Mathematics Subject Classification: 46B03; 03E15
The source file(s), DichotomyMinimality39.tex: 214179 bytes, is(are)
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From alspach at www.math.okstate.edu Tue Nov 13 10:39:34 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200711131639.lADGdYot036773 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by W. Kubis
Status: R
This is an announcement for the paper "Fraisse sequences -- a
category-theoretic approach to universal homogeneous structures"
by W. Kubis.
Abstract: We present a category-theoretic approach to universal
homogeneous objects, with applications in the theory of Banach
spaces and in set-theoretic topology.
Archive classification: math.CT math.FA math.GN
Mathematics Subject Classification: Primary: 18A22, 18A23; Secondary:
54C15, 46B04, 46B26.
Remarks: This is a first draft, announcing the main results. Some
proofs/comments are missing. More complete version will be coming soon.
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0711.1683
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From banach-bounces at math.okstate.edu Tue Nov 13 21:11:24 2007
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Date: Tue, 13 Nov 2007 21:11:36 -0600
From: Dale Alspach <alspach at math.okstate.edu>
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Subject: [Banach] New Book
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Status: R
Biorthogonal Systems in Banach Spaces
Springer
Series: CMS Books in Mathematics
Authors: Hajek, P., Montesinos Santalucia, V., Vanderwerff, J., Zizler, V.
ISBN: 978-0-387-68914-2
The main theme of this book is the relation between the global structure
of Banach spaces and the various types of generalized "coordinate
systems" - or "bases" - they possess. This subject is not new and has
been investigated since the inception of the study of Banach spaces. In
this book, the authors systematically investigate the concepts of
Markushevich bases, fundamental systems, total systems and their
variants. The material naturally splits into the case of separable
Banach spaces, as is treated in the first two chapters, and the
nonseparable case, which is covered in the remainder of the book. This
book contains new results, and a substantial portion of this material
has never before appeared in book form. The book will be of interest to
both researchers and graduate students.
Topics covered in this book include:
- Biorthogonal Systems in Separable Banach Spaces
- Universality and Szlenk Index
- Weak Topologies and Renormings
- Biorthogonal Systems in Nonseparable Spaces
- Transfinite Sequence Spaces
- Applications
Petr Hajek is Professor of Mathematics at the Mathematical Institute of
the Academy of Sciences of the Czech Republic. Vicente Montesinos is
Professor of Mathematics at the Polytechnic University of
Valencia, Spain. Jon Vanderwerff is Professor of Mathematics at La
Sierra University, in Riverside, California. Vaclav Zizler is Professor
of Mathematics at the Mathematical Institute of the Academy of Sciences
of the Czech Republic.
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Date: Wed, 14 Nov 2007 11:36:12 -0800 (PST)
From: Robert Phelps <phelps at math.washington.edu>
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Cc: josepedro.moreno at uam.es
Subject: [Banach] Important open problems
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Status: R
Our colleague Jose Pedro (Pepe) Moreno in Madrid would greatly appreciate
getting your suggestions for the most important open problems in functional
analysis or Banach space theory. His address is josepedro.moreno at uam.es
Bob Phelps
University of Washington
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From alspach at www.math.okstate.edu Wed Nov 14 21:36:16 2007
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To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Uffe Haagerup and Magdalena Musat
Status: R
This is an announcement for the paper "The Effros-Ruan conjecture
for bilinear forms on C$^*$-algebras" by Uffe Haagerup and Magdalena
Musat.
Abstract: In 1991 Effros and Ruan conjectured that a certain
Grothendieck-type inequality for a bilinear form on C$^*$-algebras
holds if (and only if) the bilinear form is jointly completely
bounded. In 2002 Pisier and Shlyakhtenko proved that this inequality
holds in the more general setting of operator spaces, provided that
the operator spaces in question are exact. Moreover, they proved
that the conjecture of Effros and Ruan holds for pairs of C$^*$-algebras,
of which at least one is exact. In this paper we prove that the
Effros-Ruan conjecture holds for general C$^*$-algebras, with
constant one. More precisely, we show that for every jointly
completely bounded (for short, j.c.b.) bilinear form on a pair of
C$^*$-algebras $A$ and $B$\,, there exist states $f_1$\,, $f_2$ on
$A$ and $g_1$\,, $g_2$ on $B$ such that for all $a\in A$ and $b\in
B$\,, \begin{equation*} |u(a, b)|\leq
\|u\|_{jcb}(f_1(aa^*)^{1/2}g_1(b^*b)^{1/2}+f_2(a^*a)^{1/2}g_2(bb^*)^{1/2})\,.
\end{equation*} While the approach by Pisier and Shlyakhtenko relies
on free probability techniques, our proof uses more classical
operator algebra theory, namely, Tomita-Takesaki theory and special
properties of the Powers factors of type III$_\lambda$\,, $0<
\lambda< 1$\,.
Archive classification: math.OA math.FA
Mathematics Subject Classification: 46L10; 47L25
Remarks: 18 pages
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Submitted from: mmusat at memphis.edu
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From alspach at www.math.okstate.edu Fri Nov 23 16:07:54 2007
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Subject: Abstract of a paper by P.G. Casazza, S.J. Dilworth, E. Odell, Th.Schlumprecht, and Andras Zsak
Status: R
This is an announcement for the paper "Coefficient quantization for
frames in Banach spaces" by P.G. Casazza, S.J. Dilworth, E. Odell,
Th.Schlumprecht, and Andras Zsak.
Abstract: Let $(e_i)$ be a fundamental system of a Banach space.
We consider the problem of approximating linear combinations of
elements of this system by linear combinations using quantized
coefficients. We will concentrate on systems which are possibly
redundant. Our model for this situation will be frames in Banach
spaces.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B20, 41A6
Remarks: 33 pages
The source file(s), cqpf.tex: 90407 bytes, is(are) stored in gzipped
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file has gzipped size 173kb.
Submitted from: schlump at math.tamu.edu
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From banach-bounces at math.okstate.edu Wed Dec 5 06:50:06 2007
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Date: Tue, 04 Dec 2007 10:26:48 -0500
From: Artem Zvavitch <zvavitch at math.kent.edu>
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Subject: [Banach] Summer school on,
"Fourier analytic and probabilistic methods in geometric functional,
analysis and convexity"
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Dear Colleagues,
We would like to invite you to participate in the summer school on
"Fourier analytic and probabilistic methods in geometric functional
analysis and convexity" in August 13-20, 2008.
The school is being organized by the NSF funded Focused Research Group
collaborative project on the same subject
(http://www.math.ucdavis.edu/~geofunction/). It is oriented towards
graduate students, postdocs and researchers who wish to get an
introduction to the subject. The school will feature several series's
of lectures. Confirmed speakers include
Alexander Barvinok (University of Michigan),
Piotr Indyk (Massachusetts Institute of Technology),
Fedor Nazarov (University of Wisconsin-Madison),
Krzysztof Oleszkiewicz (University of Warsaw),
Rolf Schneider (University of Freiburg),
Santosh S. Vempala (Georgia Institute of Technology).
The school will be hosted by the Department of Mathematical Sciences at
Kent State University in August 13-20, 2008. Kent is located in the
suburbs of Cleveland, Ohio, where summers are quite beautiful. We plan
to spend one of the evenings at the nearby Blossom Music Center, the
summer home of the renowned Cleveland Orchestra.
With NSF funding we will be able to cover local, and, probably, travel
expenses for a limited number of participants, so we ask you to reply as
soon as possible to Dmitry Ryabogin (ryabogin at math.kent.edu) or Artem
Zvavitch (zvavitch at math.kent.edu). Graduate students and Postdoctoral
fellows are especially encouraged to apply.
For further information and breaking news, please, consult
http://www.math.kent.edu/math/FAPR.cfm
Again, please note that your early response will help us gauge the needs
for housing, lecture room(s), etc. We hope to be sending out information
regarding housing by the end of December.
We hope to see you in Kent next August.
Best Regards,
The organizing committee
Alex Koldobsky
Mark Rudelson
Dmitry Ryabogin
Stanislaw Szarek
Roman Vershynin
Elisabeth Werner
Artem Zvavitch
_______________________________________________
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Subject: [Banach] Conference on Applied Mathematics and Approximation Theory
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--===============0911927567==
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International Conference on Applied Mathematics and Approximation Theory
2008,
October 11-13,2008, University of Memphis, Memphis, TN, USA.
Honoring 80th Birthday of P.L.Butzer (AMAT08).
Plenary Speakers:C.Bardaro, J.Bona, B.Berndt, F.Deutsch, K.Diethelm,
S.Dragomir,
J.Goldstein, M.Ismail, M.J.Lai, H.Mhaskar, J.Prestin, S.Samko, R.Stens,
A.Zayed.
Organizer:George Anastassiou,
http://www.msci.memphis.edu/AMAT2008/
--===============0911927567==
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_______________________________________________
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--===============0911927567==--
From alspach at www.math.okstate.edu Sat Dec 8 17:01:03 2007
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From: Dale Alspach <alspach at www.math.okstate.edu>
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To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jarno Talponen
Status: R
This is an announcement for the paper "Convex-transitivity and
function spaces" by Jarno Talponen.
Abstract: It is shown that the Bochner space L^{p}([0,1],X) is
convex-transitive for any convex-transitive X and 1\leq p\leq \infty.
If H is an infinite-dimensional Hilbert space and C_{0}(L) is
convex-transitive, then C_{0}(L,H) is convex-transitive. Some new
fairly concrete examples of convex-transitive spaces are provided.
Archive classification: math.FA
Mathematics Subject Classification: 46B04; 46E40
The source file(s), Rotations3.tex: 62608 bytes, is(are) stored in
gzipped form as 0711.3768.gz with size 19kb. The corresponding
postcript file has gzipped size 119kb.
Submitted from: talponen at cc.helsinki.fi
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0711.3768
or
http://arXiv.org/abs/0711.3768
or by email in unzipped form by transmitting an empty message with
subject line
uget 0711.3768
or in gzipped form by using subject line
get 0711.3768
to: math at arXiv.org.
From alspach at www.math.okstate.edu Sat Dec 8 17:05:10 2007
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Date: Sat, 8 Dec 2007 17:05:09 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200712082305.lB8N596o018971 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by R.Haydon, E.Odell, Th.Schlumprecht
Status: R
This is an announcement for the paper "Small subspaces of L_p" by
R.Haydon, E.Odell, Th.Schlumprecht.
Abstract: We prove that if $X$ is a subspace of $L_p$ $(2<p<\infty)$
then either $X$ embeds isomorphically into $\ell_p \oplus \ell_2$
or $X$ contains a subspace $Y$, which is isomorphic to $\ell_p(\ell_2)$.
We also give an intrinsic characterization of when $X$ embeds into
$\ell_p \oplus \ell_2$ in terms of weakly null trees in $X$ or
equivalently in terms of the ``infinite asymptotic game'' played
in $X$. This solves problems concerning small subspaces of $L_p$
originating in the 1970's. The techniques used were developed over
several decades, the most recent being that of weakly null trees
developed in the 2000's.
Archive classification: math.FA
Mathematics Subject Classification: 46E30
The source file(s), smallsubspaces.tex: 99982 bytes, is(are) stored
in gzipped form as 0711.3919.gz with size 31kb. The corresponding
postcript file has gzipped size 185kb.
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/0711.3919
or
http://arXiv.org/abs/0711.3919
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uget 0711.3919
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to: math at arXiv.org.
From alspach at www.math.okstate.edu Sat Dec 8 17:07:26 2007
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Date: Sat, 8 Dec 2007 17:07:26 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200712082307.lB8N7QLp019002 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by J. G. Christensen and G. Olafsson
Status: R
This is an announcement for the paper "Coorbit spaces for dual
pairs" by J. G. Christensen and G. Olafsson.
Abstract: This paper contains a generalization of the coorbit space
theory initiated in the 1980's by H.G. Feichtinger and K.H. Groechenig.
This theory has been a powerful tool in characterizing Banach spaces
of functions with the use of integrable representations of locally
compact groups. Examples are a wavelet characterization of the Besov
spaces and a characterization of some Bergman spaces by the discrete
series representation of $\mathrm{SL}_2(\mathbb{R})$. We suggest a
generalization of the coorbit space theory, which is able to account
for a wider range of Banach spaces and also for quasi Banach spaces.
A few examples of Banach spaces which could not be covered by the
previous theory are described.
Archive classification: math.FA math.RT
Mathematics Subject Classification: 43A15,42B35 (Primary) 22D12
(Secondary)
The source file(s), coorbit.bbl: 4205 bytes
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0711.4120
or
http://arXiv.org/abs/0711.4120
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uget 0711.4120
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to: math at arXiv.org.
From alspach at www.math.okstate.edu Sat Dec 8 17:09:26 2007
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Date: Sat, 8 Dec 2007 17:09:26 -0600 (CST)
From: Dale Alspach <alspach at www.math.okstate.edu>
Message-Id: <200712082309.lB8N9Q0J019035 at www.math.okstate.edu>
To: alspach at www.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Yuri I. Lyubich
Status: R
This is an announcement for the paper "Upper bound for isometric
embeddings \ell_2^m\to\ell_p^n" by Yuri I. Lyubich.
Abstract: The isometric embeddings $\ell_{2;K}^m\to\ell_{p;K}^n$
($m\geq 2$, $p\in 2\N$) over a field $K\in{R, C, H}$ are considered,
and an upper bound for the minimal $n$ is proved. In the commutative
case ($K\neq H$) the bound was obtained by Delbaen, Jarchow and
Pe{\l}czy{\'n}ski (1998) in a different way.
Archive classification: math.FA
Mathematics Subject Classification: 46B04
Remarks: 5 pages
The source file(s), upbound.bbl: 1810 bytes
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0712.0214
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http://arXiv.org/abs/0712.0214
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