Messages from 2010
These are the messages distributed to the Banach list during 2010.
From alspach at fourier.math.okstate.edu Thu Jan 7 14:28:09 2010
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To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Romain Demazeux
Message-Id: <20100107202809.08059D0B0B at fourier.math.okstate.edu>
Date: Thu, 7 Jan 2010 14:28:08 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Weighted composition operators
as Daugavet centers" by Romain Demazeux.
Abstract: We investigate the norm identity $\|uC_\varphi + T\| =
\|u\|_\infty + \|T\|$ for classes of operators on $C(S)$, where $S$
is a compact Hausdorff space without isolated point, and characterize
those weighted composition operators which satisfy this equation
for every weakly compact operator $T : C(S)\to C(S)$. We also give a
characterization of such weighted composition operator acting on the
disk algebra $A(D).$
Archive classification: math.FA
Mathematics Subject Classification: 47B33, 47B38,46E15
Remarks: 18 pages
The source file(s),
Weighted_composition_operators_as_Daugavet_centers.tex: 57655 bytes,
is(are) stored in gzipped form as 0912.4032.gz with size 15kb. The
corresponding postcript file has gzipped size 112kb.
Submitted from: romain.demazeux at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0912.4032
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http://arXiv.org/abs/0912.4032
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to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu Jan 7 14:29:09 2010
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id 3D21AD0B0B; Thu, 7 Jan 2010 14:29:09 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Shuheng Zhou
Message-Id: <20100107202909.3D21AD0B0B at fourier.math.okstate.edu>
Date: Thu, 7 Jan 2010 14:29:09 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Restricted eigenvalue conditions
on subgaussian random matrices" by Shuheng Zhou.
Abstract: It is natural to ask: what kinds of matrices satisfy the
Restricted Eigenvalue (RE) condition? In this paper, we associate the
RE condition (Bickel-Ritov-Tsybakov 09) with the complexity of a subset
of the sphere in $\R^p$, where $p$ is the dimensionality of the data,
and show that a class of random matrices with independent rows, but
not necessarily independent columns, satisfy the RE condition, when
the sample size is above a certain lower bound. Here we explicitly
introduce an additional covariance structure to the class of random
matrices that we have known by now that satisfy the Restricted Isometry
Property as defined in Candes and Tao 05 (and hence the RE condition),
in order to compose a broader class of random matrices for which the RE
condition holds. In this case, tools from geometric functional analysis
in characterizing the intrinsic low-dimensional structures associated
with the RE condition has been crucial in analyzing the sample complexity
and understanding its statistical implications for high dimensional data.
Archive classification: math.ST math.FA stat.ML stat.TH
Remarks: 23 Pages
The source file(s), graphs.tex: 71862 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0912.4045
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http://arXiv.org/abs/0912.4045
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From alspach at fourier.math.okstate.edu Thu Jan 7 14:30:08 2010
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id E1269D0B0B; Thu, 7 Jan 2010 14:30:08 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Daniel Li, Herve Queffelec, Luis Rodriguez-Piazza
Message-Id: <20100107203008.E1269D0B0B at fourier.math.okstate.edu>
Date: Thu, 7 Jan 2010 14:30:08 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Some new thin sets of integers in
Harmonic Analysis" by Daniel Li, Herve Queffelec, Luis Rodriguez-Piazza.
Abstract: We randomly construct various subsets $\Lambda$ of the integers
which have both smallness and largeness properties. They are small since
they are very close, in various meanings, to Sidon sets: the continuous
functions with spectrum in $\Lambda$ have uniformly convergent series,
and their Fourier coefficients are in $\ell_p$ for all $p>1$; moreover,
all the Lebesgue spaces $L^q_\Lambda$ are equal for $q<+\infty$. On
the other hand, they are large in the sense that they are dense in the
Bohr group and that the space of the bounded functions with spectrum in
$\Lambda$ is non separable. So these sets are very different from the
thin sets of integers previously known.
Archive classification: math.FA
Mathematics Subject Classification: MSC: Primary: 42A36 ; 42A44 ; 42A55 ;
42A61 ; 43A46; Secondary:
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0912.4214
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http://arXiv.org/abs/0912.4214
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From alspach at fourier.math.okstate.edu Thu Jan 7 14:30:42 2010
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id 1A472D0B0B; Thu, 7 Jan 2010 14:30:42 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Mark Kozdoba
Message-Id: <20100107203042.1A472D0B0B at fourier.math.okstate.edu>
Date: Thu, 7 Jan 2010 14:30:42 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On the smallest L_2 projection
of a curve in R^n" by Mark Kozdoba.
Abstract: For a curve T:[0,1] -> R^n, we consider the directions theta
in R^n which T "misses" the most and quantify this, as a function of
the L_2 norm of T's differential.
Archive classification: math.FA
The source file(s), curvL2arch.tex: 21640 bytes, is(are) stored in
gzipped form as 0912.5323.gz with size 8kb. The corresponding postcript
file has gzipped size 79kb.
Submitted from: marikk at tx.technion.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0912.5323
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http://arXiv.org/abs/0912.5323
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to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu Jan 7 14:31:33 2010
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id 85B63D0B0B; Thu, 7 Jan 2010 14:31:33 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Mohammed Yahdi
Message-Id: <20100107203133.85B63D0B0B at fourier.math.okstate.edu>
Date: Thu, 7 Jan 2010 14:31:33 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A coanalytic rank on super-ergodic
operators" by Mohammed Yahdi.
Abstract: Techniques from Descriptive Set Theory are applied in order
to study the Topological Complexity of families of operators naturally
connected to ergodic operators in infinite dimensional Banach Spaces. The
families of ergodic, uniform-ergodic,Cesaro-bounded and power-bounded
operators are shown to be Borel sets, while the family of super-ergodic
operators is shown to be either coanalytic or Borel according to
specific structures of the Space. Moreover, trees and coanalytic ranks
are introduced to characterize super-ergodic operators as well as spaces
where the above classes of operators do not coincide.
Archive classification: math.GN math.FA
Mathematics Subject Classification: 47A35; 54H05
Remarks: 9 pages
The source file(s), YahdiCoanalyticRankOnSuperErgodicOperators.tex:
28531 bytes, is(are) stored in gzipped form as 0912.5389.gz with size
9kb. The corresponding postcript file has gzipped size 80kb.
Submitted from: myahdi at ursinus.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0912.5389
or
http://arXiv.org/abs/0912.5389
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From alspach at fourier.math.okstate.edu Thu Jan 7 14:37:03 2010
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id 5918FD0B0B; Thu, 7 Jan 2010 14:37:03 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by F. Baudier, N. J. Kalton, and G. Lancien
Message-Id: <20100107203703.5918FD0B0B at fourier.math.okstate.edu>
Date: Thu, 7 Jan 2010 14:37:03 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A new metric invariant for Banach
spaces" by F. Baudier, N. J. Kalton, and G. Lancien.
Abstract: We show that if the Szlenk index of a Banach space $X$
is larger than the first infinite ordinal $\omega$ or if the Szlenk
index of its dual is larger than $\omega$, then the tree of all finite
sequences of integers equipped with the hyperbolic distance metrically
embeds into $X$. We show that the converse is true when $X$ is assumed
to be reflexive. As an application, we exhibit new classes of Banach
spaces that are stable under coarse-Lipschitz embeddings and therefore
under uniform homeomorphisms.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B20; 46T99
Remarks: 22 pages
The source file(s), new_invariant_BKL.tex: 63462 bytes, is(are) stored in
gzipped form as 0912.5113.gz with size 19kb. The corresponding postcript
file has gzipped size 132kb.
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/0912.5113
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http://arXiv.org/abs/0912.5113
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to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu Jan 7 14:38:19 2010
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id 9156CD0B0B; Thu, 7 Jan 2010 14:38:19 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Piotr Indyk and Stanislaw Szarek
Message-Id: <20100107203819.9156CD0B0B at fourier.math.okstate.edu>
Date: Thu, 7 Jan 2010 14:38:19 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A simple construction of
almost-Euclidean subspaces of $\ell_1^N$ via tensor products" by Piotr
Indyk and Stanislaw Szarek.
Abstract: It has been known since 1970's that the N-dimensional
$\ell_1$-space contains nearly Euclidean subspaces whose dimension
is $\Omega(N)$. However, proofs of existence of such subspaces
were probabilistic, hence non-constructive, which made the results
not-quite-suitable for subsequently discovered applications to
high-dimensional nearest neighbor search, error-correcting codes over
the reals, compressive sensing and other computational problems. In this
paper we present a "low-tech" scheme which, for any $a > 0$, allows to
exhibit nearly Euclidean $\Omega(N)$-dimensional subspaces of $\ell_1^N$
while using only $N^a$ random bits. Our results extend and complement
(particularly) recent work by Guruswami-Lee-Wigderson. Characteristic
features of our approach include (1) simplicity (we use only tensor
products) and (2) yielding arbitrarily small distortions, or "almost
Euclidean" subspaces.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 46B25, 52A21, 68P30
Remarks: 10 pages
The source file(s), tensoring3e.tex: 37038 bytes, is(are) stored in
gzipped form as 1001.0041.gz with size 13kb. The corresponding postcript
file has gzipped size 99kb.
Submitted from: szarek at cwru.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1001.0041
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http://arXiv.org/abs/1001.0041
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From alspach at fourier.math.okstate.edu Thu Jan 7 14:39:05 2010
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id BCAFFD0B0B; Thu, 7 Jan 2010 14:39:05 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Jaegil Kim and Shlomo Reisner
Message-Id: <20100107203905.BCAFFD0B0B at fourier.math.okstate.edu>
Date: Thu, 7 Jan 2010 14:39:05 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Local minimality of the
volume-product at the simplex" by Jaegil Kim and Shlomo Reisner.
Abstract: It is proved that the simplex is a strict local minimum for
the volume-product P(K)=min vol(K)vol(K^z), in the Banach-Mazur space of
n-dimensional (classes of ) convex bodies. Here K^z is the polar body
of K about the point z and the minimum is taken over all the points
z in the interior of K. Linear local stability in the neighborhood of
the simplex is proved as well. In the proof, methods that were recently
introduced by Nazarov, Petrov, Ryabogin and Zvavitch are extended to
the non-symmetric setting.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 52A40
The source file(s), KR-loc-min-simplex.tex: 34954 bytes, is(are) stored in
gzipped form as 1001.0217.gz with size 12kb. The corresponding postcript
file has gzipped size 84kb.
Submitted from: reisner at math.haifa.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1001.0217
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http://arXiv.org/abs/1001.0217
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From alspach at fourier.math.okstate.edu Thu Jan 7 14:40:07 2010
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id 290F9D0B0B; Thu, 7 Jan 2010 14:40:07 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Narinder S Claire
Message-Id: <20100107204007.290F9D0B0B at fourier.math.okstate.edu>
Date: Thu, 7 Jan 2010 14:40:07 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The spectral mapping theorem"
by Narinder S Claire.
Abstract: We prove the Spectral Mapping Theorem for the
Helffer-Sj\"ostrand functional calculus for linear operators on Banach
spaces with real spectra and consequently give a new proof for the
Spectral Mapping Theorem for self-adjoint operators on Hilbert spaces.
Archive classification: math.SP math.FA
Mathematics Subject Classification: 47A60
Remarks: latex 12 pages
The source file(s), integral.eps: 33099 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1001.0232
or
http://arXiv.org/abs/1001.0232
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uget 1001.0232
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to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu Jan 7 14:40:48 2010
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id 6E01FD0B0B; Thu, 7 Jan 2010 14:40:48 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu
Subject: Abstract of a paper by Vyacheslav V. Chistyakov and Yuliya V. Tretyachenko
Message-Id: <20100107204048.6E01FD0B0B at fourier.math.okstate.edu>
Date: Thu, 7 Jan 2010 14:40:48 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Maps of several variables of finite
total variation and Helly-type selection principles" by Vyacheslav
V. Chistyakov and Yuliya V. Tretyachenko.
Abstract: Given a map from a rectangle in the n-dimensional real Euclidean
space into a metric semigroup, we introduce a concept of the total
variation, which generalizes a similar concept due to T. H. Hildebrandt
(1963) for real functions of two variables and A. S. Leonov (1998) for
real functions of n variables, and study its properties. We show that the
total variation has many classical properties of Jordan's variation such
as the additivity, generalized triangle inequality and sequential lower
semicontinuity. We prove two variants of a pointwise selection principle
of Helly-type, one of which is as follows: a pointwise precompact sequence
of metric semigroup valued maps on the rectangle, whose total variations
are uniformly bounded, admits a pointwise convergent subsequence.
Archive classification: math.FA
Mathematics Subject Classification: 26B30 (Primary); 20M15; 28A20
(Secondary)
Remarks: 47 pages, LaTeX, uses elsarticle.sty
The source file(s), HSP_arX.tex: 126875 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1001.0451
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http://arXiv.org/abs/1001.0451
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From alspach at fourier.math.okstate.edu
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Subject: [Banach] Conference Announcement
From: Dale Alspach <alspach at math.okstate.edu>
Date: Fri, 08 Jan 2010 15:55:38 -0600
To: banach at math.okstate.edu
The 6th Conference on Function Spaces will be held at the SIUE campus near
St. Louis between May 17 and May 22, 2010. More information may be found
at:
http://www.siue.edu/MATH/conference2010/
The organizer received a small grant to defray the attendance cost;
according to the NSF rules priority will be given to young mathematicians
(including graduate students) without other sources of support.
Krzysztof Jarosz
Department of Mathematics and Statistics
Southern Illinois University Edwardsville
Edwardsville, IL 62026-1653, USA
tel.: (618) 650-2354
fax: (618) 650-3771
e-mail: kjarosz at siue.edu
http://www.siue.edu/~kjarosz/
_______________________________________________
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From alspach at fourier.math.okstate.edu
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Subject: [Banach] INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE
DIESTEL (March 20-21, 2010)
From: Artem Zvavitch <zvavitch at math.kent.edu>
Date: Fri, 15 Jan 2010 11:40:15 -0500 (10:40 CST)
To: BANACH LIST <banach at math.okstate.edu>
Dear Friends,
On Saturday - Sunday, March 20-21, 2010, (best arrival date Friday,
March 19/ Departure Monday, March 22) the Department of Mathematical
Sciences at Kent State University will be famous but still very
informal. We are happy to announce an:
INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL
The following people are among speakers: Peter Casazza, Hans Jarchow,
Alexander Koldobsky, Pepe Orihuela, Olek Pelczynski, Thomas
Schlumprecht, Lutz Weis.
It would be great if you could visit Kent State and participate in the
seminar!
The conference will have a registration fee of $200
WHICH INCLUDES: pick up/drop off from the airport, THREE DAY STAY in
the Microtel hotel at Streetsboro, Saturday/Sunday lunches/dinners to be
provided at the department.
If you plan to stay fewer than 3 nights or prefer to make your own
accommodation arrangements, please reduce your registration fee by $45
per day that you will not use our hotel arrangements.
If possible, please send a check for your registration fee, made out to
the Department of Mathematical Sciences, Kent State University. The
check should be mailed to Virginia Wright, Department of Mathematical
Sciences, Kent State University, Kent, OH, 44242. The fee can be also
be paid during the registration (check/cash).
The conference is supported by NSF; The Department of Mathematical
Sciences and Kent State University. Depending on funds availability the
fee may be waived for young researchers and people without available
funding. Please, write as soon as possible to zvavitch at math.kent.edu
May we ask you to respond as soon as February 19
(zvavitch at math.kent.edu), so that we can gauge the need for housing,
lecture room(s), etc.
Best Regards,
Analysis group at Kent State!
_______________________________________________
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From alspach at fourier.math.okstate.edu
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Subject: [Banach] Workshop at A&M
From: Bill Johnson <johnson at math.tamu.edu>
Date: Mon, 15 Feb 2010 10:45:52 -0600 (CST)
To: banach at math.okstate.edu
Workshop in Analysis and Probability
Department of Mathematics
Texas A&M University
2010
Rostislav Grigorchuk (chair) and Oleg Musin are organizing a one day
Workshop on "Asymptotic and Extreme
Properties of Metric Spaces and Groups" for Monday, April 12. This meeting
is directed to asymptotic and extreme properties of metric spaces,
manifolds, groups, and groupoids. The home page for this Workshop is at
http://www.math.tamu.edu/~grigorch/conf/2010workshop.html
The Summer 2010 Workshop in Analysis and Probability at Texas A&M
University will be in session from July 6 until August 1. For information
about the Workshop, consult the Workshop Home Page, whose new URL is
http://www.math.tamu.edu/conferences/linanalysis/
The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held
July 30 - August 1.
Michael Anshelevich (chair), Jinho Baik, and Roland Speicher are
organizing
a Concentration Week on "Orthogonal Polynomials in Probability Theory" for
the week of July 6-10. The theme of this Concentration Week is orthogonal
polynomial techniques in probability theory, especially in the study of
random matrices, free probability, and multiple stochastic integrals. Baik
and Speicher will give mini-courses designed to introduce non specialists
to these topics. The home page for this Concentration Week is at
http://www.math.tamu.edu/~manshel/OPPT/main.html
Ilijas Farah and David Kerr (chair) are organizing a Concentration Week
on "Set Theory and Functional Analysis" for the week of July 26-30. The
broad theme will be recent applications of set theory in functional
analysis, with emphasis on combinatorial phenomena and classifiability
problems in operator algebras, dynamics, and Banach space theory. The
program will include lecture series by Christian Rosendal, David Sherman,
and Todor Tsankov. The home page for this Concentration Week is at
http://www.math.tamu.edu/~kerr/concweek10/index.html
The Workshop is supported in part by grants from the National Science
Foundation (NSF). Minorities, women, graduate students, and young
researchers are especially encouraged to attend.
For logistical support, including requests for support, please contact
Cara Barton <cara at math.tamu.edu>. For more information on the Workshop
itself, please contact William Johnson <johnson at math.tamu.edu>, David
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 meeting "Asymptotic and Extreme
Properties of Metric Spaces and Groups", contact Rostislav Grigorchuk
<grigorch at math.tamu.edu>.
For information about the Concentration Week "Orthogonal Polynomials in
Probability Theory", contact Michael Anshelevich <manshel at math.tamu.edu>.
For information about the Concentration Week "Set Theory and Functional
Analysis", contact David Kerr <kerr at math.tamu.edu>.
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Fri Mar 5 12:47:52 2010
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id D6667D0BA7; Fri, 5 Mar 2010 12:47:52 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Mathieu Meyer, Carsten Schutt and Elisabeth M. Werner
Message-Id: <20100305184752.D6667D0BA7 at fourier.math.okstate.edu>
Date: Fri, 5 Mar 2010 12:47:52 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A convex body whose centroid
and Santalo point are far apart" by Mathieu Meyer, Carsten Schutt and
Elisabeth M. Werner.
Abstract: We give an example of a convex body whose centroid and Santal\'o
point are ``far apart".
Archive classification: math.FA
Mathematics Subject Classification: 52A20, 53A15
The source file(s), symmetrie25-12-09.tex: 65533 bytes, is(are) stored in
gzipped form as 1001.0714.gz with size 16kb. The corresponding postcript
file has gzipped size 84kb.
Submitted from: elisabeth.werner at case.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1001.0714
or
http://arXiv.org/abs/1001.0714
or by email in unzipped form by transmitting an empty message with
subject line
uget 1001.0714
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From alspach at fourier.math.okstate.edu Fri Mar 5 12:48:47 2010
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id A342DD0BA7; Fri, 5 Mar 2010 12:48:47 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Matthew Daws
Message-Id: <20100305184847.A342DD0BA7 at fourier.math.okstate.edu>
Date: Fri, 5 Mar 2010 12:48:47 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A bicommutant theorem for dual
Banach algebras" by Matthew Daws.
Abstract: A dual Banach algebra is a Banach algebra which is a dual space,
with the multiplication being separately weak$^*$-continuous. We show that
given a unital dual Banach algebra $\mc A$, we can find a reflexive Banach
space $E$, and an isometric, weak$^*$-weak$^*$-continuous homomorphism
$\pi:\mc A\to\mc B(E)$ such that $\pi(\mc A)$ equals its own bicommutant.
Archive classification: math.FA
Mathematics Subject Classification: 46H05, 46H15, 47L10
Remarks: 6 pages
The source file(s), dba.tex: 23544 bytes, is(are) stored in gzipped
form as 1001.1146.gz with size 8kb. The corresponding postcript file
has gzipped size 84kb.
Submitted from: matt.daws at cantab.net
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1001.1146
or
http://arXiv.org/abs/1001.1146
or by email in unzipped form by transmitting an empty message with
subject line
uget 1001.1146
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to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Mar 5 12:49:53 2010
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X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 9A00ED0BA7; Fri, 5 Mar 2010 12:49:53 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Enrique A. Sanchez Perez and Dirk Werner
Message-Id: <20100305184953.9A00ED0BA7 at fourier.math.okstate.edu>
Date: Fri, 5 Mar 2010 12:49:53 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The geometry of L^p-spaces over
atomless measure spaces and the Daugavet property" by Enrique A. Sanchez
Perez and Dirk Werner.
Abstract: We show that $L^p$-spaces over atomless measure spaces can be
characterized in terms of a $p$-concavity type geometric property that
is related with the Daugavet property.
Archive classification: math.FA
Mathematics Subject Classification: 46B04; 46B25
The source file(s), LpDaugavet7.tex: 44923 bytes, is(are) stored in
gzipped form as 1001.1262.gz with size 14kb. The corresponding postcript
file has gzipped size 84kb.
Submitted from: werner at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1001.1262
or
http://arXiv.org/abs/1001.1262
or by email in unzipped form by transmitting an empty message with
subject line
uget 1001.1262
or in gzipped form by using subject line
get 1001.1262
to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Mar 5 12:51:03 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id BCFD4D0BA7; Fri, 5 Mar 2010 12:51:03 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Nigel J. Kalton and Marisa Zymonopoulou
Message-Id: <20100305185103.BCFD4D0BA7 at fourier.math.okstate.edu>
Date: Fri, 5 Mar 2010 12:51:03 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Positive definite distributions
and normed spaces" by Nigel J. Kalton and Marisa Zymonopoulou.
Abstract: We answer a question of Alex Koldobsky on isometric embeddings
of finite dimensional normed spaces.
Archive classification: math.FA
Mathematics Subject Classification: 52A21
The source file(s), zymnotes4.tex: 71037 bytes, is(are) stored in gzipped
form as 1001.1412.gz with size 21kb. The corresponding postcript file
has gzipped size 84kb.
Submitted from: marisa.zym at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1001.1412
or
http://arXiv.org/abs/1001.1412
or by email in unzipped form by transmitting an empty message with
subject line
uget 1001.1412
or in gzipped form by using subject line
get 1001.1412
to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Mar 5 12:53:53 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 9C670D0BA7; Fri, 5 Mar 2010 12:53:53 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by F. Sukochev and D. Zanin
Message-Id: <20100305185353.9C670D0BA7 at fourier.math.okstate.edu>
Date: Fri, 5 Mar 2010 12:53:53 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Khinchin inequality and Banach-Saks
type properties in rearrangement-invariant spaces" by F. Sukochev
and D. Zanin.
Abstract: \begin{abstract} {\it We study the class of all
rearrangement-invariant (=r.i.)
function spaces $E$ on $[0,1]$ such that there exists $0<q<1$ for
which $
\Vert \sum_{_{k=1}}^n\xi_k\Vert _{E}\leq Cn^{q}$, where $\{\xi_k\}_{k\ge
1}\subset E$ is an arbitrary sequence of independent identically
distributed symmetric random variables on $[0,1]$ and $C>0$ does not
depend on $n$. We completely characterize all Lorentz spaces having this
property and complement classical results of Rodin and Semenov for Orlicz
spaces $exp(L_p)$, $p\ge 1$. We further apply our results to the study
of Banach-Saks index sets in r.i. spaces. \end{abstract}
Archive classification: math.FA
Mathematics Subject Classification: 46E30 (46B09 46B20)
Citation: Studia Math. 191 (2009), no. 2, 101--122
The source file(s), sukochev_zanin_submitted.tex: 67832 bytes, is(are)
stored in gzipped form as 1001.2432.gz with size 20kb. The corresponding
postcript file has gzipped size 84kb.
Submitted from: zani0005 at csem.flinders.edu.au
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1001.2432
or
http://arXiv.org/abs/1001.2432
or by email in unzipped form by transmitting an empty message with
subject line
uget 1001.2432
or in gzipped form by using subject line
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to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Mar 5 12:54:34 2010
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X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 59A17D0BA7; Fri, 5 Mar 2010 12:54:34 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Ellen Veomett and Kevin Wildrick
Message-Id: <20100305185434.59A17D0BA7 at fourier.math.okstate.edu>
Date: Fri, 5 Mar 2010 12:54:34 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Spaces of small metric cotype"
by Ellen Veomett and Kevin Wildrick.
Abstract: Naor and Mendel's metric cotype extends the notion of the
Rademacher cotype of a Banach space to all metric spaces. Every Banach
space has metric cotype at least 2. We show that any metric space that
is bi-Lipschitz equivalent to an ultrametric space has infinimal metric
cotype 1. We discuss the invariance of metric cotype inequalities under
snowflaking mappings and Gromov-Hausdorff limits, and use these facts
to establish a partial converse of the main result.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 30L05; 46B85
Remarks: 21 pages
The source file(s), MetricCotype8.bbl: 3780 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1001.3326
or
http://arXiv.org/abs/1001.3326
or by email in unzipped form by transmitting an empty message with
subject line
uget 1001.3326
or in gzipped form by using subject line
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to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Mar 5 12:55:40 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 8F91ED0BA7; Fri, 5 Mar 2010 12:55:40 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by David Cruz-Uribe, Jose Maria Martell, and Carlos Perez
Message-Id: <20100305185540.8F91ED0BA7 at fourier.math.okstate.edu>
Date: Fri, 5 Mar 2010 12:55:40 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Sharp weighted estimates for
classical operators" by David Cruz-Uribe, Jose Maria Martell, and
Carlos Perez.
Abstract: We give a new proof of the sharp one weight $L^p$ inequality
for any operator $T$ that can be approximated by Haar shift operators
such as the Hilbert transform, any Riesz transform, the Beurling-Ahlfors
operator. Our proof avoids the Bellman function technique and two weight
norm inequalities. We use instead a recent result due to A. Lerner to
estimate the oscillation of dyadic operators. Our method is flexible
enough to prove the corresponding sharp one-weight norm inequalities
for some operators of harmonic analysis: the maximal singular integrals
associated to $T$, Dyadic square functions and paraproducts, and the
vector-valued maximal operator of C. Fefferman-Stein. Also we can derive
a very sharp two-weight bump type condition for $T$.
Archive classification: math.CA math.FA
Mathematics Subject Classification: 42B20; 42B25
The source file(s), dyadic-hilbert.tex: 72598 bytes, is(are) stored in
gzipped form as 1001.4254.gz with size 21kb. The corresponding postcript
file has gzipped size 84kb.
Submitted from: carlosperez at us.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1001.4254
or
http://arXiv.org/abs/1001.4254
or by email in unzipped form by transmitting an empty message with
subject line
uget 1001.4254
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to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Mar 5 12:58:52 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 9DE14D0BA7; Fri, 5 Mar 2010 12:58:52 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Antonio Aviles, Grzegorz Plebanek, and Jose Rodriguez
Message-Id: <20100305185852.9DE14D0BA7 at fourier.math.okstate.edu>
Date: Fri, 5 Mar 2010 12:58:52 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The McShane integral in weakly
compactly generated spaces" by Antonio Aviles, Grzegorz Plebanek,
and Jose Rodriguez.
Abstract: Di Piazza and Preiss asked whether every Pettis integrable
function defined on [0,1] and taking values in a weakly compactly
generated Banach space is McShane integrable. In this paper we answer
this question in the negative.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 28B05; 46B10; 46B26
The source file(s), McShaneWCGFinal.tex: 53304 bytes, is(are) stored in
gzipped form as 1001.4896.gz with size 16kb. The corresponding postcript
file has gzipped size 84kb.
Submitted from: avileslo at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1001.4896
or
http://arXiv.org/abs/1001.4896
or by email in unzipped form by transmitting an empty message with
subject line
uget 1001.4896
or in gzipped form by using subject line
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to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Mar 5 13:00:17 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id CA1DED0BA7; Fri, 5 Mar 2010 13:00:17 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Paul F.X. Mueller and Markus Passenbrunner
Message-Id: <20100305190017.CA1DED0BA7 at fourier.math.okstate.edu>
Date: Fri, 5 Mar 2010 13:00:17 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A representation theorem for
singular integral operators on spaces of homogeneous type" by Paul
F.X. Mueller and Markus Passenbrunner.
Abstract: Let (X,d,\mu) be a space of homogeneous type and E a UMD
Banach space. Under the assumption mu({x})=0 for all x in X, we prove a
representation theorem for singular integral operators on (X,d,mu) as a
series of simple shifts and rearrangements plus two paraproducts. This
gives a T(1) Theorem in this setting.
Archive classification: math.FA
Mathematics Subject Classification: 42B20; 60G42; 46E40; 47B38
The source file(s), Basis.eps: 11807 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1001.4926
or
http://arXiv.org/abs/1001.4926
or by email in unzipped form by transmitting an empty message with
subject line
uget 1001.4926
or in gzipped form by using subject line
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to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Mar 5 13:01:19 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
Delivered-To: alspach at fourier.math.okstate.edu
Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 2B534D0BA7; Fri, 5 Mar 2010 13:01:19 -0600 (CST)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Aicke Hinrichs and Jan Vybiral
Message-Id: <20100305190119.2B534D0BA7 at fourier.math.okstate.edu>
Date: Fri, 5 Mar 2010 13:01:19 -0600 (CST)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Johnson-Lindenstrauss lemma for
circulant matrices" by Aicke Hinrichs and Jan Vybiral.
Abstract: We prove a variant of a Johnson-Lindenstrauss lemma for
matrices with circulant structure. This approach allows to minimise
the randomness used, is easy to implement and provides good running
times. The price to be paid is the higher dimension of the target
space $k=O(\varepsilon^{-2}\log^3n)$ instead of the classical bound
$k=O(\varepsilon^{-2}\log n)$.
Archive classification: math.FA cs.IT math.IT
Mathematics Subject Classification: 52C99; 68Q01
The source file(s), Hinrichs_Vybiral.tex: 18930 bytes, is(are) stored in
gzipped form as 1001.4919.gz with size 7kb. The corresponding postcript
file has gzipped size 84kb.
Submitted from: jan.vybiral at oeaw.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1001.4919
or
http://arXiv.org/abs/1001.4919
or by email in unzipped form by transmitting an empty message with
subject line
uget 1001.4919
or in gzipped form by using subject line
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to: math at arXiv.org.
Return-path: <banach-bounces at math.okstate.edu>
Subject: [Banach] Conference "Banach Space Geometry"
From: astashkn at ssu.samara.ru
Date: Mon, 22 Mar 2010 20:47:38 +0500 (UZT)
To: banach at math.okstate.edu
First Announcement for the conference
"Banach Space Geometry",
in honor of Evgeny Semenov's 70th birthday,
to be held September 5--11, 2010 at the Euler
International Mathematical Institute in
Saint-Petersburg, Russia.
We would like to announce that the website
for the conference
http://www.pdmi.ras.ru/EIMI/2010/bsg/1ann.html
has been updated and now includes visa information
and preliminary list of participants.
Sincerely yours,
Sergey Astashkin,
Sergey Novikov
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Mon Mar 22 13:10:14 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id F158CD0D17; Mon, 22 Mar 2010 13:10:13 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Simon Foucart, Alain Pajor, Holger Rauhut, and Tino Ullrich
Message-Id: <20100322181013.F158CD0D17 at fourier.math.okstate.edu>
Date: Mon, 22 Mar 2010 13:10:13 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The Gelfand widths of
$\ell_p$-balls for $0<p\leq 1$" by Simon Foucart, Alain Pajor, Holger
Rauhut, and Tino Ullrich.
Abstract: We provide sharp lower and upper bounds for the Gelfand widths
of $\ell_p$-balls in the $N$-dimensional $\ell_q^N$-space for $0<p\leq 1$
and $p<q \leq 2$. Such estimates are highly relevant to the novel theory
of compressive sensing, and our proofs rely on methods from this area.
Archive classification: math.FA cs.IT math.IT
Mathematics Subject Classification: 41A46, 46B09
Remarks: 15 pages
The source file(s), GelfandSAHTarxiv.tex: 45830 bytes, is(are) stored in
gzipped form as 1002.0672.gz with size 15kb. The corresponding postcript
file has gzipped size 84kb.
Submitted from: tino.ullrich at hcm.uni-bonn.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1002.0672
or
http://arXiv.org/abs/1002.0672
or by email in unzipped form by transmitting an empty message with
subject line
uget 1002.0672
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to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Mar 22 13:12:06 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
Delivered-To: alspach at fourier.math.okstate.edu
Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id D10A5D0D17; Mon, 22 Mar 2010 13:12:06 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Necip Simsek
Message-Id: <20100322181206.D10A5D0D17 at fourier.math.okstate.edu>
Date: Mon, 22 Mar 2010 13:12:06 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On some geometric properties of
sequence space defined by de la Vallee-Poussin mean" by Necip Simsek.
Abstract: In this work, we investigate k-nearly uniform convex(k-NUC)
and the uniform Opial properties of the sequence space defined by de
la Vallee-Poussin mean. Also we give some corollaries concerning the
geometrical properties of this space.
Archive classification: math.FA
Mathematics Subject Classification: 46A45, 46B20, 46B45
Remarks: 9 pages, no figure
The source file(s), Manuscript-arXiv.tex: 29046 bytes, is(are) stored in
gzipped form as 1002.1498.gz with size 8kb. The corresponding postcript
file has gzipped size 84kb.
Submitted from: nsimsek at adiyaman.edu.tr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1002.1498
or
http://arXiv.org/abs/1002.1498
or by email in unzipped form by transmitting an empty message with
subject line
uget 1002.1498
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to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Mar 22 13:13:15 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
Delivered-To: alspach at fourier.math.okstate.edu
Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id AB315D0D17; Mon, 22 Mar 2010 13:13:15 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Constantinos Kardaras and Gordan Zitkovic
Message-Id: <20100322181315.AB315D0D17 at fourier.math.okstate.edu>
Date: Mon, 22 Mar 2010 13:13:15 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Forward-convex convergence of
sequences in $\mathbb{L}^0_+$" by Constantinos Kardaras and Gordan
Zitkovic.
Abstract: For a sequence in $\mathbb{L}^0_+$, we provide simple
necessary and sufficient conditions to ensure that each sequence of
its forward convex combinations converges to the same limit. These
conditions correspond to a measure-free version of the notion of uniform
integrability and are related to the numeraire problem of mathematical
finance.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 46A16; 46E30; 60A10
Remarks: 14 pages
The source file(s), fcc.bbl: 3371 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1002.1889
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From alspach at fourier.math.okstate.edu Mon Mar 22 13:14:29 2010
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id 64AF9D0D17; Mon, 22 Mar 2010 13:14:29 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Jan Vybiral
Message-Id: <20100322181429.64AF9D0D17 at fourier.math.okstate.edu>
Date: Mon, 22 Mar 2010 13:14:29 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A variant of the
Johnson-Lindenstrauss lemma for circulant matrices" by Jan Vybiral.
Abstract: We continue our study of the Johnson-Lindenstrauss lemma and
its connection to circulant matrices started in \cite{HV}. We reduce
the bound on $k$ from $k=O(\varepsilon^{-2}\log^3n)$ proven there to
$k=O(\varepsilon^{-2}\log^2n)$. Our technique differs essentially from
the one used in \cite{HV}. We employ the discrete Fourier transform and
singular value decomposition to deal with the dependency caused by the
circulant structure.
Archive classification: math.FA
Mathematics Subject Classification: 52C99, 68Q01
The source file(s), Johnson_Lind2.tex: 21785 bytes, is(are) stored in
gzipped form as 1002.2847.gz with size 8kb. The corresponding postcript
file has gzipped size 84kb.
Submitted from: jan.vybiral at oeaw.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1002.2847
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http://arXiv.org/abs/1002.2847
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From alspach at fourier.math.okstate.edu Mon Mar 22 13:15:41 2010
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id BF8F0D0D17; Mon, 22 Mar 2010 13:15:41 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Tuomas Hyt\"onen and Mikko Kemppainen
Message-Id: <20100322181541.BF8F0D0D17 at fourier.math.okstate.edu>
Date: Mon, 22 Mar 2010 13:15:41 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On the relation of Carleson's
embedding and the maximal theorem in the context of Banach space
geometry" by Tuomas Hyt\"onen and Mikko Kemppainen.
Abstract: Hyt\"onen, McIntosh and Portal (J. Funct. Anal., 2008) proved
two vector-valued generalizations of the classical Carleson embedding
theorem, both of them requiring the boundedness of a new vector-valued
maximal operator, and the other one also the type p property of the
underlying Banach space as an assumption. We show that these conditions
are also necessary for the respective embedding theorems, thereby
obtaining new equivalences between analytic and geometric properties of
Banach spaces.
Archive classification: math.FA
Mathematics Subject Classification: 42B25 (Primary) 46E40 (Secondary)
Remarks: 10 pages
The source file(s), carleson.bbl: 2240 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1002.2876
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http://arXiv.org/abs/1002.2876
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From alspach at fourier.math.okstate.edu Mon Mar 22 13:20:56 2010
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id C864CD0D17; Mon, 22 Mar 2010 13:20:56 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Rui Liu and Bentuo Zheng
Message-Id: <20100322182056.C864CD0D17 at fourier.math.okstate.edu>
Date: Mon, 22 Mar 2010 13:20:56 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A characterization of Schauder
frames which are near-Schauder bases" by Rui Liu and Bentuo Zheng.
Abstract: A basic problem of interest in connection with the study
of Schauder frames in Banach spaces is that of characterizing those
Schauder frames which can essentially be regarded as Schauder bases. In
this paper, we give a solution to this problem using the notion of
the minimal-associated sequence spaces and the minimal-associated
reconstruction operators for Schauder frames. We prove that a Schauder
frame is a near-Schauder basis if and only if the kernel of the
minimal-associated reconstruction operator contains no copy of $c_0$. In
particular, a Schauder frame of a Banach space with no copy of $c_0$
is a near-Schauder basis if and only if the minimal-associated sequence
space contains no copy of $c_0$. In these cases, the minimal-associated
reconstruction operator has a finite dimensional kernel and the dimension
of the kernel is exactly the excess of the near-Schauder basis. Using
these results, we make related applications on Besselian frames and
near-Riesz bases.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B15, 46B45; Secondary 47A20.
Remarks: 12 pages
The source file(s), LZh.tex: 37398 bytes, is(are) stored in gzipped
form as 1002.3851.gz with size 11kb. The corresponding postcript file
has gzipped size 84kb.
Submitted from: leorui at mail.nankai.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1002.3851
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http://arXiv.org/abs/1002.3851
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From alspach at fourier.math.okstate.edu Mon Mar 22 13:22:32 2010
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id 29CF6D0D17; Mon, 22 Mar 2010 13:22:32 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Oleg I. Reinov
Message-Id: <20100322182232.29CF6D0D17 at fourier.math.okstate.edu>
Date: Mon, 22 Mar 2010 13:22:32 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Approximation of operators in
Banach spaces" by Oleg I. Reinov.
Abstract: It is a translation of an old paper of mine. We describe
the topology tau_p in the space Pi_p(Y,X), for which the closures of
convex sets in tau_p and in *-weak topology of the space Pi_p(Y,X) are
coincident. Thereafter, we investigate some properties of the space Pi_p,
related to this new topology. 2010-remark: Occasionally, the topology
is coincides with the lambda_p-topology from the paper "Compact operators
which factor through subspaces of l_p", Math. Nachr. 281(2008), 412-423
by Deba Prasad Sinha and Anil Kumar Karn.
Archive classification: math.FA
Mathematics Subject Classification: 46B28
Citation: In the collection "Primenenie funkcional'nogo analiza v teorii
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1002.3902
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http://arXiv.org/abs/1002.3902
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From alspach at fourier.math.okstate.edu Mon Mar 22 13:23:50 2010
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id B3814D0D17; Mon, 22 Mar 2010 13:23:50 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Daniel Carando and Daniel Galicer
Message-Id: <20100322182350.B3814D0D17 at fourier.math.okstate.edu>
Date: Mon, 22 Mar 2010 13:23:50 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Natural symmetric tensor norms"
by Daniel Carando and Daniel Galicer.
Abstract: In the spirit of the work of Grothendieck, we introduce and
study natural symmetric n-fold tensor norms. We prove that there are
exactly six natural symmetric tensor norms for $n\ge 3$, a noteworthy
difference with the 2-fold case in which there are four. Using a symmetric
version of a result of Carne we also describe which natural symmetric
tensor norms preserve Banach algebras.
Archive classification: math.FA
Mathematics Subject Classification: 46M05
Remarks: 11 pages
The source file(s), Natural22.tex: 42738 bytes, is(are) stored in gzipped
form as 1002.3950.gz with size 12kb. The corresponding postcript file
has gzipped size 84kb.
Submitted from: dgalicer at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1002.3950
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http://arXiv.org/abs/1002.3950
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From alspach at fourier.math.okstate.edu Mon Mar 22 13:24:32 2010
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id BE655D0D17; Mon, 22 Mar 2010 13:24:32 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Mar Jimenez-Sevilla and Luis Sanchez-Gonzalez
Message-Id: <20100322182432.BE655D0D17 at fourier.math.okstate.edu>
Date: Mon, 22 Mar 2010 13:24:32 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Smooth extension of functions
on non-separable Banach spaces" by Mar Jimenez-Sevilla and Luis
Sanchez-Gonzalez.
Abstract: Let us consider a Banach space $X$ with the property that
every Lipschitz function can be uniformly approximated by Lipschitz and
$C^1$-smooth functions (this is the case either for a weakly compactly
generated Banach space $X$ with a $C^1$-smooth norm, or a Banach space
$X$ bi-Lipschitz homeomorphic to a subset of $c_0(\Gamma)$, for some
set $\Gamma$, such that the coordinate functions of the homeomorphism
are $C^1$-smooth). Then for every closed subspace $Y\subset X$ and every
$C^1$-smooth (Lipschitz) function $f:Y\to\Real$, there is a $C^1$-smooth
(Lipschitz, repectively) extension of $f$ to $X$. An analogous result
can be stated for real-valued functions defined on closed convex subsets
of $X$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 12 pages
The source file(s), draftSmoothextension220210.tex: 59770 bytes, is(are)
stored in gzipped form as 1002.4147.gz with size 15kb. The corresponding
postcript file has gzipped size 84kb.
Submitted from: lfsanche at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1002.4147
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http://arXiv.org/abs/1002.4147
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From alspach at fourier.math.okstate.edu Mon Mar 22 13:25:19 2010
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id 1BD5AD0D17; Mon, 22 Mar 2010 13:25:19 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Mehmet Orhon
Message-Id: <20100322182519.1BD5AD0D17 at fourier.math.okstate.edu>
Date: Mon, 22 Mar 2010 13:25:19 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The ideal center of the dual of
a Banach lattice" by Mehmet Orhon.
Abstract: Let $E$ be a Banach lattice. Its ideal center $Z(E)$ is embedded
naturally in the ideal center $Z(E')$ of its dual. The embedding may be
extended to a contractive algebra and lattice homomorphism of $Z(E)''$
into $Z(E')$. We show that the extension is onto $Z(E')$ if and only if
$E$ has a topologically full center. (That is, for each $x\in E$, the
closure of $Z(E)x$ is the closed ideal generated by $x$.) The result can
be generalized to the ideal center of the order dual of an Archimedean
Riesz space and in a modified form to the orthomorphisms on the order
dual of an Archimedean Riesz space.
Archive classification: math.FA
Mathematics Subject Classification: 47B38
The source file(s), center-final.tex: 25459 bytes, is(are) stored in
gzipped form as 1002.4346.gz with size 8kb. The corresponding postcript
file has gzipped size 84kb.
Submitted from: mo at unh.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1002.4346
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http://arXiv.org/abs/1002.4346
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From alspach at fourier.math.okstate.edu Mon Mar 22 13:25:59 2010
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id 30A0CD0D17; Mon, 22 Mar 2010 13:25:59 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Oleg Reinov and Qaisar Latif
Message-Id: <20100322182559.30A0CD0D17 at fourier.math.okstate.edu>
Date: Mon, 22 Mar 2010 13:25:59 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Banach spaces without approximation
properties of type p" by Oleg Reinov and Qaisar Latif.
Abstract: The main purpose of this note is to show that the question
posed in the paper of Sinha D.P. and Karn A.K.("Compact operators which
factor through subspaces of $l_p$ Math. Nachr. 281, 2008, 412-423; see the
very end of that paper) has a negative answer, and that the answer was
known, essentially, in 1985 after the papers "Approximation properties
of order p and the existence of non-p-nuclear operators with p-nuclear
second adjoints" (Math. Nachr. 109(1982), 125-134) and "Approximation of
operators in Banach spaces" (Application of functional analysis in the
approximation theory (KGU, Kalinin), 1985, 128-142) by Reinov O.I. have
been appeared in 1982 and in 1985 respectively.
Archive classification: math.FA
Mathematics Subject Classification: 46B28
Remarks: LATeX, English (4 pp.)
The source file(s), FA_J_LAT.tex: 15882 bytes, is(are) stored in gzipped
form as 1003.0085.gz with size 6kb. The corresponding postcript file
has gzipped size 84kb.
Submitted from: orein51 at mail.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.0085
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http://arXiv.org/abs/1003.0085
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From alspach at fourier.math.okstate.edu Mon Mar 22 13:27:23 2010
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id C3C32D0D17; Mon, 22 Mar 2010 13:27:23 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Ohad Giladi, Manor Mendel, and Assaf Naor
Message-Id: <20100322182723.C3C32D0D17 at fourier.math.okstate.edu>
Date: Mon, 22 Mar 2010 13:27:23 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Improved bounds in the metric
cotype inequality for Banach spaces" by Ohad Giladi, Manor Mendel,
and Assaf Naor.
Abstract: It is shown that if (X, ||.||_X) is a Banach space with
Rademacher cotype q then for every integer n there exists an even integer
m< n^{1+1/q}$ such that for every f:Z_m^n --> X we have
\sum_{j=1}^n \Avg_x [ ||f(x+ (m/2) e_j)-f(x) ||_X^q ] < C m^q
\Avg_{\e,x} [
||f(x+\e)-f(x) ||_X^q ],
where the expectations are with respect to uniformly chosen x\in
Z_m^n and
\e\in \{-1,0,1\}^n, and all the implied constants may depend only on
q and the Rademacher cotype q constant of X. This improves the bound
of m< n^{2+\frac{1}{q}} from [Mendel, Naor 2008]. The proof of the
above inequality is based on a ``smoothing and approximation" procedure
which simplifies the proof of the metric characterization of Rademacher
cotype of [Mendel, Naor 2008]. We also show that any such ``smoothing
and approximation" approach to metric cotype inequalities must require
m> n^{(1/2)+(1/q)}.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B80,46B85,51F99,05C12
Remarks: 27 pages, 1 figure
The source file(s), cotypeGMN.bbl: 3212 bytes cotypeGMN.tex: 87911 bytes
tr-jigsaw.eps: 52290 bytes tr-jigsaw.pdf: 28339 bytes, is(are) stored
in gzipped form as 1003.0279.tar.gz with size 80kb. The corresponding
postcript file has gzipped size 84kb.
Submitted from: mendelma at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.0279
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From alspach at fourier.math.okstate.edu Mon Mar 22 13:28:54 2010
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id 2CEB4D0D17; Mon, 22 Mar 2010 13:28:54 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by I. Gasparis, M.K. Papadiamantis and D.Z. Zisimopoulou
Message-Id: <20100322182854.2CEB4D0D17 at fourier.math.okstate.edu>
Date: Mon, 22 Mar 2010 13:28:54 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "More \(\ell_r\) saturated
\(\mathcal{L}_\infty\) spaces" by I. Gasparis, M.K. Papadiamantis and
D.Z. Zisimopoulou.
Abstract: We present some new examples of separable \(\mathcal_\infty\)
spaces which are \(\ell_r\) saturated for some \(1 < r < \infty\).
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 05D10
The source file(s), lrsaturatedtel.tex: 49218 bytes, is(are) stored in
gzipped form as 1003.0579.gz with size 15kb. The corresponding postcript
file has gzipped size 84kb.
Submitted from: ioagaspa at math.auth.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.0579
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http://arXiv.org/abs/1003.0579
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From alspach at fourier.math.okstate.edu Mon Mar 22 13:30:06 2010
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X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 202A7D0D17; Mon, 22 Mar 2010 13:30:06 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Spiros A. Argyros and Theocharis Raikoftsalis
Message-Id: <20100322183006.202A7D0D17 at fourier.math.okstate.edu>
Date: Mon, 22 Mar 2010 13:30:06 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The cofinal property of the
reflexive indecomposable Banach spaces" by Spiros A. Argyros and
Theocharis Raikoftsalis.
Abstract: It is shown that every separable reflexive Banach space is a
quotient of a reflexive Hereditarily Indecomposable space, which yields
that every separable reflexive Banach is isomorphic to a subspace of a
reflexive Indecomposable space. Furthermore, every separable reflexive
Banach space is a quotient of a reflexive complementably $\ell_p$
saturated space with $1<p<\infty$ and of a $c_0$ saturated space.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B06, 46B70
Remarks: 29 pages
The source file(s), Arg-Raiko-Cofinal.tex: 122453 bytes, is(are) stored in
gzipped form as 1003.0870.gz with size 36kb. The corresponding postcript
file has gzipped size 84kb.
Submitted from: sargyros at math.ntua.gr
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http://front.math.ucdavis.edu/1003.0870
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http://arXiv.org/abs/1003.0870
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From alspach at fourier.math.okstate.edu Fri Apr 2 14:43:28 2010
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id 17E05D0D19; Fri, 2 Apr 2010 14:43:28 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by N.J. Kalton, F.A. Sukochev, and D.V. Zanin
Message-Id: <20100402194328.17E05D0D19 at fourier.math.okstate.edu>
Date: Fri, 2 Apr 2010 14:43:28 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Orbits in symmetric spaces,
II by N.J. Kalton, F.A. Sukochev, and D.V. Zanin.
Abstract: Suppose $E$ is fully symmetric Banach function space on
$(0,1)$ or $(0,\infty)$ or a fully symmetric Banach sequence space. We
give necessary and sufficient conditions on $f\in E$ so that its orbit
$\Omega(f)$ is the closed convex hull of its extreme points. We also
give an application to symmetrically normed ideals of compact operators
on a Hilbert space.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46B70, 46B20
Submitted from: zani0005 at csem.flinders.edu.au
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.1817
or
http://arxiv.org/abs/1003.1817
From alspach at fourier.math.okstate.edu Fri Apr 2 16:07:44 2010
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X-Original-To: alspach
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id AE197D0D19; Fri, 2 Apr 2010 16:07:44 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by S.V. Astashkin, D.V. Zanin, E.M. Semenov, F.A. Sukochev
Message-Id: <20100402210744.AE197D0D19 at fourier.math.okstate.edu>
Date: Fri, 2 Apr 2010 16:07:44 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Kruglov operator and operators
defined by random permutations" by S.V. Astashkin, D.V. Zanin,
E.M. Semenov, and F.A. Sukochev.
Abstract: The Kruglov property and the Kruglov operator play an important
role in the study of geometric properties of r.i. function spaces. We
prove that the boundedness of the Kruglov operator in a r.i. space is
equivalent to the uniform boundedness on this space of a sequence of
operators defined by random permutations. It is shown also that there
is no minimal r.i. space with the Kruglov property.
Archive classification: math.FA
Mathematics Subject Classification: 46E30
Remarks: translated from original Russian text
Submitted from: zani0005 at csem.flinders.edu.au
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.2009
or
http://arXiv.org/abs/1003.2009
From alspach at fourier.math.okstate.edu Fri Apr 2 16:17:59 2010
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id 73E3BD0D19; Fri, 2 Apr 2010 16:17:59 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Mark Rudelson and Roman Vershynin
Message-Id: <20100402211759.73E3BD0D19 at fourier.math.okstate.edu>
Date: Fri, 2 Apr 2010 16:17:59 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Non-asymptotic theory of random
matrices: extreme singular values" by Mark Rudelson and Roman Vershynin.
Abstract: The classical random matrix theory is mostly focused on
asymptotic spectral properties of random matrices as their dimensions
grow to infinity. At the same time many recent applications from convex
geometry to functional analysis to information theory operate with random
matrices in fixed dimensions. This survey addresses the non-asymptotic
theory of extreme singular values of random matrices with independent
entries. We focus on recently developed geometric methods for estimating
the hard edge of random matrices (the smallest singular value).
Archive classification: math.FA
Mathematics Subject Classification: 46B09; 60B20
Remarks: Submission for International Congress of Mathematicians,
Hydebabad, India, 2010
Submitted from: romanv at umich.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.2990
or
http://arXiv.org/abs/1003.2990
From alspach at fourier.math.okstate.edu Thu Apr 8 16:38:59 2010
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id 5B514D0D27; Thu, 8 Apr 2010 16:38:59 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Miguel Martin, Javier Meri, Mikhail Popov, and Beata Randrianantoanina
Message-Id: <20100408213859.5B514D0D27 at fourier.math.okstate.edu>
Date: Thu, 8 Apr 2010 16:38:59 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Numerical index of absolute
sums of Banach spaces" by Miguel Martin, Javier Meri, Mikhail Popov,
and Beata Randrianantoanina.
Abstract: We study the numerical index of absolute sums of Banach spaces,
giving general conditions which imply that the numerical index of the sum
is less or equal than the infimum of the numerical indices of the summands
and we provide some examples where the equality holds covering the already
known case of $c_0$-, $\ell_1$- and $\ell_\infty$-sums and giving as
a new result the case of $E$-sums where $E$ has the RNP and $n(E)=1$
(in particular for finite-dimensional $E$ with $n(E)=1$). We also show
that the numerical index of a Banach space $Z$ which contains a dense
increasing union of one-complemented subspaces is greater or equal than
the limit superior of the numerical indices of those subspaces. Using
these results, we give a detailed short proof of the already known fact
that the numerical indices of all infinite-dimensional $L_p(\mu)$-spaces
coincide.
Archive classification: math.FA
Remarks: 19 pages
Submitted from: randrib at muohio.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.3269
or
http://arXiv.org/abs/1003.3269
From alspach at fourier.math.okstate.edu Thu Apr 8 16:41:37 2010
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id B8B59D0D27; Thu, 8 Apr 2010 16:41:37 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Assaf Naor
Message-Id: <20100408214137.B8B59D0D27 at fourier.math.okstate.edu>
Date: Thu, 8 Apr 2010 16:41:37 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: RO
This is an announcement for the paper "L_1 embeddings of the Heisenberg
group and fast estimation of graph isoperimetry" by Assaf Naor.
Abstract: We survey connections between the theory of bi-Lipschitz
embeddings and the Sparsest Cut Problem in combinatorial optimization. The
story of the Sparsest Cut Problem is a striking example of the deep
interplay between analysis, geometry, and probability on the one hand, and
computational issues in discrete mathematics on the other. We explain how
the key ideas evolved over the past 20 years, emphasizing the interactions
with Banach space theory, geometric measure theory, and geometric group
theory. As an important illustrative example, we shall examine recently
established connections to the the structure of the Heisenberg group,
and the incompatibility of its Carnot-Carath\'eodory geometry with the
geometry of the Lebesgue space $L_1$.
Archive classification: math.MG cs.DS math.FA
Remarks: To appear in Proceedings of the International Congress of
Mathematicians, Hyderabad India, 2010
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.4261
or
http://arXiv.org/abs/1003.4261
From alspach at fourier.math.okstate.edu Thu Apr 8 16:44:00 2010
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id BCDB8D0D27; Thu, 8 Apr 2010 16:44:00 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Tetiana V. Bosenko
Message-Id: <20100408214400.BCDB8D0D27 at fourier.math.okstate.edu>
Date: Thu, 8 Apr 2010 16:44:00 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: RO
This is an announcement for the paper "Daugavet centers and direct sums
of Banach spaces" by Tetiana V. Bosenko.
Abstract: A linear continuous nonzero operator G:X->Y is a Daugavet
center if every rank-1 operator T:X->Y satisfies ||G+T||=||G||+||T||. We
study the case when either X or Y is a sum $X_1 \oplus_F X_2$ of two
Banach spaces $X_1$ and $X_2$ by some two-dimensional Banach space F. We
completely describe the class of those F such that for some spaces $X_1$
and $X_2$ there exists a Daugavet center acting from $X_1\oplus_F X_2$,
and the class of those F such that for some pair of spaces $X_1$ and
$X_2$ there is a Daugavet center acting into $X_1\oplus_F X_2$. We also
present several examples of such Daugavet centers.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B04; secondary 46B20, 46B40
Remarks: 13 pages
Submitted from: t.bosenko at mail.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.4857
or
http://arXiv.org/abs/1003.4857
From alspach at fourier.math.okstate.edu Thu Apr 8 16:45:44 2010
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id 567BCD0D27; Thu, 8 Apr 2010 16:45:44 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Guillaume Aubrun, Stanislaw Szarek and Elisabeth Werner
Message-Id: <20100408214544.567BCD0D27 at fourier.math.okstate.edu>
Date: Thu, 8 Apr 2010 16:45:44 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: RO
This is an announcement for the paper "Hastings' additivity counterexample
via Dvoretzky's theorem" by Guillaume Aubrun, Stanislaw Szarek and
Elisabeth Werner.
Abstract: The goal of this note is to show that Hastings' counterexample
to the additivity of minimal output von Neumann entropy can be readily
deduced from a sharp version of Dvoretzky's theorem on almost spherical
sections of convex bodies.
Archive classification: quant-ph math.FA
Remarks: 11 pages
Submitted from: szarek at cwru.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.4925
or
http://arXiv.org/abs/1003.4925
From alspach at fourier.math.okstate.edu Thu Apr 8 17:03:32 2010
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id A5FE3D0D27; Thu, 8 Apr 2010 17:03:32 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Hermann Pfitzner
Message-Id: <20100408220332.A5FE3D0D27 at fourier.math.okstate.edu>
Date: Thu, 8 Apr 2010 17:03:32 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: RO
This is an announcement for the paper "Phillips' Lemma for L-embedded
Banach spaces" by Hermann Pfitzner.
Abstract: In this note the following version of Phillips' lemma is
proved. The L-projection of an L-embedded space - that is of a Banach
space which is complemented in its bidual such that the norm between the
two complementary subspaces is additive - is weak-weakly sequentially
continuous.
Archive classification: math.FA
Remarks: accepted by Archiv der Mathematik, The original publication
will be available at www.springerlink.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.5088
or
http://arXiv.org/abs/1003.5088
From alspach at fourier.math.okstate.edu Thu Apr 15 10:17:10 2010
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id E9677D0D26; Thu, 15 Apr 2010 10:17:10 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Mikhail I. Ostrovskii
Message-Id: <20100415151710.E9677D0D26 at fourier.math.okstate.edu>
Date: Thu, 15 Apr 2010 10:17:10 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Weak$^*$ closures and derived
sets in dual Banach spaces" by Mikhail I. Ostrovskii.
Abstract: The main results of the paper: {\bf (1)} The dual Banach
space $X^*$ contains a linear subspace $A\subset X^*$ such that the
set $A^{(1)}$ of all limits of weak$^*$ convergent bounded nets in
$A$ is a proper norm-dense subset of $X^*$ if and only if $X$ is a
non-quasi-reflexive Banach space containing an infinite-dimensional
subspace with separable dual. {\bf (2)} Let $X$ be a non-reflexive
Banach space. Then there exists a convex subset $A\subset X^*$ such that
$A^{(1)}\neq {\overline{A}\,}^*$ (the latter denotes the weak$^*$ closure
of $A$). {\bf (3)} Let $X$ be a quasi-reflexive Banach space and $A\subset
X^*$ be an absolutely convex subset. Then $A^{(1)}={\overline{A}\,}^*$.
Archive classification: math.FA
Mathematics Subject Classification: primary 46B10; secondary 46B15; 46B20
Submitted from: ostrovsm at stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.5176
or
http://arXiv.org/abs/1003.5176
From alspach at fourier.math.okstate.edu Thu Apr 15 10:18:58 2010
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id D407CD0D26; Thu, 15 Apr 2010 10:18:58 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Constantinos Kardaras
Message-Id: <20100415151858.D407CD0D26 at fourier.math.okstate.edu>
Date: Thu, 15 Apr 2010 10:18:58 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Strictly positive support points
of convex sets in $\mathbb{L}^0_+$" by Constantinos Kardaras.
Abstract: We introduce the concept of strictly positive support points
of convex sets in $\mathbb{L}^0_+$, the nonnegative orthant of the
topological vector space $\mathbb{L}^0$ of all random variables built over
a probability space. Traditional functional-analytic definitions fail,
due to the fact that the topological dual of $\mathbb{L}^0$ is trivial
when the underlying probability space is nonatomic. A necessary and
sufficient condition for an element of a convex set in $\mathbb{L}^0_+$
to be a strictly positive support point of the set is given, inspired
from ideas in financial mathematics.
Archive classification: math.FA math.PR
Remarks: 8 pages
Submitted from: langostas at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.5419
or
http://arXiv.org/abs/1003.5419
From alspach at fourier.math.okstate.edu Thu Apr 15 10:20:04 2010
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id C0CFCD0D26; Thu, 15 Apr 2010 10:20:04 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Philip A. H. Brooker
Message-Id: <20100415152004.C0CFCD0D26 at fourier.math.okstate.edu>
Date: Thu, 15 Apr 2010 10:20:04 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Operator ideals associated with
the Szlenk index" by Philip A. H. Brooker.
Abstract: For $\alpha$ an ordinal, we investigate the class
$\mathscr{SZ}_\alpha$ consisting of all operators whose Szlenk index
is an ordinal not exceeding $\omega^\alpha$. Our main result is that
$\mathscr{SZ}_\alpha$ is a closed, injective, surjective operator ideal
for each $\alpha$. We also study the relationship between the classes
$\mathscr{SZ}_\alpha$ and several well-known closed operator ideals.
Archive classification: math.FA
Submitted from: philip.brooker at anu.edu.au
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.5706
or
http://arXiv.org/abs/1003.5706
From alspach at fourier.math.okstate.edu Thu Apr 15 10:21:34 2010
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id CC76BD0D26; Thu, 15 Apr 2010 10:21:34 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Philip A. H. Brooker
Message-Id: <20100415152134.CC76BD0D26 at fourier.math.okstate.edu>
Date: Thu, 15 Apr 2010 10:21:34 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Direct sums and the Szlenk index"
by Philip A. H. Brooker.
Abstract: For $\alpha$ an ordinal and $1<p<\infty$, we determine
a necessary and sufficient condition for an $\ell_p$-direct sum of
operators to have Szlenk index not exceeding $\omega^\alpha$. It
follows from our results that the Szlenk index of an $\ell_p$-direct
sum of operators is determined in a natural way by the behaviour of the
$\varepsilon$-Szlenk indices of its summands. Our methods give similar
results for $c_0$-direct sums.
Archive classification: math.FA
Submitted from: philip.brooker at anu.edu.au
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.5708
or
http://arXiv.org/abs/1003.5708
From alspach at fourier.math.okstate.edu Thu Apr 15 10:22:48 2010
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id 6E8B1D0D26; Thu, 15 Apr 2010 10:22:48 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Philip A. H. Brooker
Message-Id: <20100415152248.6E8B1D0D26 at fourier.math.okstate.edu>
Date: Thu, 15 Apr 2010 10:22:48 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Factorisation properties and
space ideals associated with the Szlenk index" by Philip A. H. Brooker.
Abstract: For $\alpha$ an ordinal, we study factorisation properties of
the operator ideal $\mathscr{SZ}_\alpha$ of $\alpha$-Szlenk operators. We
obtain quantitative factorisation results for Asplund operators in
terms of the Szlenk index and a partial characterisation of those
ordinals $\alpha$ for which $\mathscr{SZ}_\alpha$ has the factorisation
property. Our investigations lead to the study of a class of space ideals
defined in terms of a renorming property involving the Szlenk index.
Archive classification: math.FA
Submitted from: philip.brooker at anu.edu.au
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1003.5710
or
http://arXiv.org/abs/1003.5710
From alspach at fourier.math.okstate.edu Thu Apr 15 10:24:18 2010
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id 0AFB3D0D26; Thu, 15 Apr 2010 10:24:17 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Hermann Pfitzner
Message-Id: <20100415152418.0AFB3D0D26 at fourier.math.okstate.edu>
Date: Thu, 15 Apr 2010 10:24:17 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The dual of a non-reflexive
L-embedded Banach space contains $\ell^\infty$ isometrically." by
Hermann Pfitzner.
Abstract: See title. (A Banach space is said to be L-embedded if
it is complemented in its bidual such that the norm between the two
complementary subspaces is additive.)
Archive classification: math.FA
Remarks: accepted by Bull. Pol. Acad. Sci.
Submitted from: Hermann.Pfitzner at univ-orleans.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1004.0203
or
http://arXiv.org/abs/1004.0203
From alspach at fourier.math.okstate.edu Fri Apr 30 13:59:49 2010
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id 5F934D0D2D; Fri, 30 Apr 2010 13:59:49 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Michael Dore and Olga Maleva
Message-Id: <20100430185949.5F934D0D2D at fourier.math.okstate.edu>
Date: Fri, 30 Apr 2010 13:59:49 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A compact universal
differentiability set with Hausdorff dimension one" by Michael Dore and
Olga Maleva.
Abstract: We give a short proof that any non-zero Euclidean space
has a compact subset of Hausdorff dimension one that contains a
differentiability point of every real-valued Lipschitz function defined
on the space.
Archive classification: math.FA math.CA
Remarks: 11 pages
Submitted from: o.maleva at bham.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1004.2151
or
http://arXiv.org/abs/1004.2151
From alspach at fourier.math.okstate.edu Fri Apr 30 14:01:23 2010
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id 8B1EBD0D2D; Fri, 30 Apr 2010 14:01:23 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Bernhard G. Bodmann, Peter G. Casazza, Vern I. Paulsen, and Darrin Speegle
Message-Id: <20100430190123.8B1EBD0D2D at fourier.math.okstate.edu>
Date: Fri, 30 Apr 2010 14:01:23 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Spanning and independence
properties of frame partitions" by Bernhard G. Bodmann, Peter G. Casazza,
Vern I. Paulsen, and Darrin Speegle.
Abstract: We answer a number of open problems in frame theory concerning
the decomposition of frames into linearly independent and/or spanning
sets. We prove that in finite dimensional Hilbert spaces, Parseval frames
with norms bounded away from 1 can be decomposed into a number of sets
whose complements are spanning, where the number of these sets only
depends on the norm bound. We also prove, assuming the Kadison-Singer
conjecture is true, that this holds for infinite dimensional Hilbert
spaces. Further, we prove a stronger result for Parseval frames whose
norms are uniformly small, which shows that in addition to the spanning
property, the sets can be chosen to be independent, and the complement
of each set to contain a number of disjoint, spanning sets.
Archive classification: math.FA math.OA
Submitted from: vern at math.uh.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1004.2446
or
http://arXiv.org/abs/1004.2446
From alspach at fourier.math.okstate.edu Fri Apr 30 14:03:10 2010
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id 84D41D0D2D; Fri, 30 Apr 2010 14:03:10 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Daniel Pellegrino and Joedson Santos
Message-Id: <20100430190310.84D41D0D2D at fourier.math.okstate.edu>
Date: Fri, 30 Apr 2010 14:03:10 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A generalized unified Pietsch
domination theorem and applications" by Daniel Pellegrino and Joedson
Santos.
Abstract: This paper has a twofold purpose. Firstly, we provide
a new version of the Pietsch Domination Theorem that contains all
the previous versions (to the best of our knowledge) as particular
cases; our second goal is to characterize the arbitrary nonlinear
mappings $f:X_{1}\times\cdots\times X_{n}\rightarrow Y$ that satisfy
a quite natural Pietsch Domination-type theorem around a given point
$(a_{1},...,a_{n})\in$ $X_{1}\times\cdots\times X_{n};$ as it will be
shown, the new Pietsch Domination-type theorem plays a crucial role in
this task. The characterization of such mappings lead to the idea of a
kind of weighted summability for arbitrary mappings.
Archive classification: math.FA
Remarks: 12 pages
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1004.2643
or
http://arXiv.org/abs/1004.2643
From alspach at fourier.math.okstate.edu Fri Apr 30 14:07:44 2010
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id 02A6AD0D2D; Fri, 30 Apr 2010 14:07:43 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Roman Vershynin
Message-Id: <20100430190744.02A6AD0D2D at fourier.math.okstate.edu>
Date: Fri, 30 Apr 2010 14:07:43 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "How close is the sample covariance
matrix to the actual covariance matrix?" by Roman Vershynin.
Abstract: Given a distribution in R^n, a classical estimator of its
covariance matrix is the sample covariance matrix obtained from a
sample of N independent points. What is the optimal sample size N =
N(n) that guarantees estimation with a fixed accuracy in the operator
norm? Suppose the distribution is supported in a centered Euclidean
ball of radius \sqrt{n}. We conjecture that the optimal sample size is
N = O(n) for all distributions with finite fourth moment, and we prove
this up to an iterated logarithmic factor. This problem is motivated
by the optimal theorem of Rudelson which states that N = O(n \log n)
for distributions with finite second moment, and a recent result of
Adamczak, Litvak, Pajor and Tomczak-Jaegermann which guarantees that N =
O(n) for sub-exponential distributions.
Archive classification: math.PR math.FA math.ST stat.TH
Mathematics Subject Classification: 60H12, 60B20, 46B09
Remarks: 34 pages
Submitted from: romanv at umich.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1004.3484
or
http://arXiv.org/abs/1004.3484
From alspach at fourier.math.okstate.edu Fri Apr 30 14:09:01 2010
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id 91675D0D2D; Fri, 30 Apr 2010 14:09:01 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by M.E.Shirokov
Message-Id: <20100430190901.91675D0D2D at fourier.math.okstate.edu>
Date: Fri, 30 Apr 2010 14:09:01 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Characterization of convex
$\mu$-compact sets" by M.E.Shirokov.
Abstract: The class of $\mu$-compact sets can be considered as a natural
extension of the class of compact metrizable subsets of locally convex
spaces, to which the particular results well known for compact sets can
be generalized. This class contains all compact sets as well as many
noncompact sets widely used in applications. In this paper we give a
characterization of a convex $\mu$-compact set in terms of properties of
functions defined on this set. Namely, we prove that the class of convex
$\mu$-compact sets can be characterized by continuity of the operation
of convex closure of a function (= the double Fenchel transform) with
respect to monotonic pointwise converging sequences of continuous bounded
and of lower semicontinuous lower bounded functions.
Archive classification: math.FA math.GM
Citation: Russian Mathematical Surveys, 2008, 63:5
Remarks: 7 pages
Submitted from: msh at mi.ras.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1004.3792
or
http://arXiv.org/abs/1004.3792
From alspach at fourier.math.okstate.edu Fri Apr 30 14:10:33 2010
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id 3A7E1D0D2D; Fri, 30 Apr 2010 14:10:33 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Ohad Giladi and Assaf Naor
Message-Id: <20100430191033.3A7E1D0D2D at fourier.math.okstate.edu>
Date: Fri, 30 Apr 2010 14:10:33 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Improved bounds in the scaled
Enflo type inequality for Banach spaces" by Ohad Giladi and Assaf Naor.
Abstract: It is shown that if (X,||.||_X) is a Banach space with
Rademacher type p \ge 1, then for every integer n there exists an even
integer m < Cn^{2-1/p}log n (C is an absolute constant), such that for
every f:Z_m^n --> X, \Avg_{x,\e}[||f(x+ m\e/2)-f(x)}||_X^p] < C(p,X)
m^p\sum_{j=1}^n\Avg_x[||f(x+e_j)-f(x)||_X^p], where the expectation is
with respect to uniformly chosen x \in Z_m^n and \e \in \{-1,1\}^n, and
C(p,X) is a constant that depends on p and the Rademacher type constant of
X. This improves a bound of m < Cn^{3-2/p} that was obtained in [Mendel,
Naor 2007]. The proof is based on an augmentation of the ``smoothing
and approximation'' scheme, which was implicit in [Mendel, Naor 2007].
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B07, 46B20, 51F99
Submitted from: giladi at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1004.4221
or
http://arXiv.org/abs/1004.4221
From alspach at fourier.math.okstate.edu Fri Apr 30 14:11:40 2010
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id E35CCD0D2D; Fri, 30 Apr 2010 14:11:40 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Asghar Rahimi and Peter Balazs
Message-Id: <20100430191140.E35CCD0D2D at fourier.math.okstate.edu>
Date: Fri, 30 Apr 2010 14:11:40 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Multipliers for p-Bessel sequences
in Banach spaces" by Asghar Rahimi and Peter Balazs.
Abstract: Multipliers have been recently introduced as operators
for Bessel sequences and frames in Hilbert spaces. These operators
are defined by a fixed multiplication pattern (the symbol) which is
inserted between the analysis and synthesis operators. In this paper,
we will generalize the concept of Bessel multipliers for p-Bessel
and p-Riesz sequences in Banach spaces. It will be shown that bounded
symbols lead to bounded operators. Symbols converging to zero induce
compact operators. Furthermore, we will give sufficient conditions for
multipliers to be nuclear operators. Finally, we will show the continuous
dependency of the multipliers on their parameters.
Archive classification: math.OA math.FA
Mathematics Subject Classification: Primary 42C40, Secondary 41A58, 47A58
Remarks: 17 pages
Submitted from: Peter.Balazs at oeaw.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1004.5212
or
http://arXiv.org/abs/1004.5212
From alspach at fourier.math.okstate.edu Thu May 20 10:18:41 2010
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id DE245D0D2E; Thu, 20 May 2010 10:18:41 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by G. Botelho, D. Diniz, V.V. Favaro and D. Pellegrino
Message-Id: <20100520151841.DE245D0D2E at fourier.math.okstate.edu>
Date: Thu, 20 May 2010 10:18:41 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Spaceability in Banach and
quasi-Banach sequence spaces" by G. Botelho, D. Diniz, V.V. Favaro and
D. Pellegrino.
Abstract: Let $X$ be a Banach space. We prove that, for a large class
of Banach or quasi-Banach spaces $E$ of $X$-valued sequences, the sets
$E-\bigcup _{q\in\Gamma}\ell_{q}(X)$, where $\Gamma$ is any subset
of $(0,\infty]$, and $E-c_{0}(X)$ contain closed infinite-dimensional
subspaces of $E$ (if non-empty, of course). This result is applied in
several particular cases and it is also shown that the same technique
can be used to improve a result on the existence of spaces formed by
norm-attaining linear operators.
Archive classification: math.FA
Mathematics Subject Classification: 46A45, 46A16, 46B45
Remarks: 9 pages
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.0596
or
http://arXiv.org/abs/1005.0596
From alspach at fourier.math.okstate.edu Thu May 20 12:34:26 2010
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id 3F1EED0D2E; Thu, 20 May 2010 12:34:26 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Pamela Gorkin and Anthony G. OFarrell
Message-Id: <20100520173426.3F1EED0D2E at fourier.math.okstate.edu>
Date: Thu, 20 May 2010 12:34:26 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Pervasive algebras and maximal
subalgebras" by Pamela Gorkin and Anthony G. O'Farrell.
Abstract: A uniform algebra $A$ on its Shilov boundary $X$ is {\em
maximal} if $A$ is not $C(X)$ and there is no uniform algebra properly
contained between $A$ and $C(X)$. It is {\em essentially pervasive}
if $A$ is dense in $C(F)$ whenever $F$ is a proper closed subset of the
essential set of $A$. If $A$ is maximal, then it is essentially pervasive
and proper. We explore the gap between these two concepts. We show the
following: (1) If $A$ is pervasive and proper, and has a nonconstant
unimodular element, then $A$ contains an infinite descending chain
of pervasive subalgebras on $X$. (2) It is possible to imbed a copy
of the lattice of all subsets of $\N$ into the family of pervasive
subalgebras of some $C(X)$. (3) In the other direction, if $A$ is
strongly logmodular, proper and pervasive, then it is maximal. (4) This
fails if the word \lq strongly' is removed. We discuss further examples,
involving Dirichlet algebras, $A(U)$ algebras, Douglas algebras, and
subalgebras of $H^\infty(\mathbb{D})$. We develop some new results that
relate pervasiveness, maximality and relative maximality to support sets
of representing measures.
Archive classification: math.FA
Mathematics Subject Classification: 46J10
Submitted from: AnthonyG.OFarrell at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.0719
or
http://arXiv.org/abs/1005.0719
From alspach at fourier.math.okstate.edu Thu May 20 12:35:55 2010
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id 2A65DD0D2E; Thu, 20 May 2010 12:35:55 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Rafal Gorak
Message-Id: <20100520173555.2A65DD0D2E at fourier.math.okstate.edu>
Date: Thu, 20 May 2010 12:35:55 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Coarse version of the Banach
Stone theorem" by Rafal Gorak.
Abstract: We show that if there exists a Lipschitz homeomorphism $T$
between the nets in the Banach spaces $C(X)$ and $C(Y)$ of continuous
real valued functions on compact spaces $X$ and $Y$, then the spaces $X$
and $Y$ are homeomorphic provided $l(T) \times l(T^{-1})<\frac{6}{5}$. By
$l(T)$ and $l(T^{-1})$ we denote the Lipschitz constants of the maps
$T$ and $T^{-1}$. This improves the classical result of Jarosz and the
recent result of Dutrieux and Kalton where the constant obtained is
$\frac{17}{16}$. We also estimate the distance of the map $T$ from the
isometry of the spaces $C(X)$ and $C(Y)$.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 46E15, 46B26, 46T99
Submitted from: R.Gorak at mini.pw.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.0937
or
http://arXiv.org/abs/1005.0937
From alspach at fourier.math.okstate.edu Thu May 20 12:37:14 2010
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id 5B542D0D2E; Thu, 20 May 2010 12:37:14 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by D. Azagra, R. Fry, and L. Keener
Message-Id: <20100520173714.5B542D0D2E at fourier.math.okstate.edu>
Date: Thu, 20 May 2010 12:37:14 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Real analytic approximation
of Lipschitz functions on Hilbert space and other Banach spaces"
by D. Azagra, R. Fry, and L. Keener.
Abstract: Let $X$ be a separable Banach space with a separating
polynomial. We show that there exists $C\geq 1$ such that for
every Lipschitz function $f:X\rightarrow\mathbb{R}$, and every
$\varepsilon>0$, there exists a Lipschitz, real analytic function
$g:X\rightarrow\mathbb{R}$ such that $|f(x)-g(x)|\leq \varepsilon$
and $\textrm{Lip}(g)\leq C\textrm{Lip}(f)$. This result is new even
in the case when $X$ is a Hilbert space. Furthermore we characterize
the class of Banach spaces having this approximation property as those
Banach spaces $X$ having a Lipschitz, real-analytic separating function
(meaning a Lipschitz, real analytic function $Q:X\to [0, +\infty)$
such that $Q(0)=0$ and $Q(x)\geq \|x\|$ for $\|x\|\geq 1$).
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 40 pages
Submitted from: dazagra at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.1050
or
http://arXiv.org/abs/1005.1050
From alspach at fourier.math.okstate.edu Thu May 20 12:39:14 2010
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id DDC32D0D2E; Thu, 20 May 2010 12:39:14 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Ondrej F.K. Kalenda
Message-Id: <20100520173914.DDC32D0D2E at fourier.math.okstate.edu>
Date: Thu, 20 May 2010 12:39:14 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Spaces not containing $\ell_1$
have weak aproximate fixed point property" by Ondrej F.K. Kalenda.
Abstract: A nonempty closed convex bounded subset $C$ of a Banach space
is said to have the weak approximate fixed point property if for every
continuous map $f:C\to C$ there is a sequence $\{x_n\}$ in $C$ such that
$x_n-f(x_n)$ converge weakly to $0$. We prove in particular that $C$
has this property whenever it contains no sequence equivalent to the
standard basis of $\ell_1$. As a byproduct we obtain a characterization
of Banach spaces not containing $\ell_1$ in terms of the weak topology.
Archive classification: math.FA
Remarks: 5 pages
Submitted from: kalenda at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.1218
or
http://arXiv.org/abs/1005.1218
From alspach at fourier.math.okstate.edu Thu May 20 12:40:39 2010
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id 65324D0D2E; Thu, 20 May 2010 12:40:39 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Anton Baranov and Yurii Belov
Message-Id: <20100520174039.65324D0D2E at fourier.math.okstate.edu>
Date: Thu, 20 May 2010 12:40:39 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Systems of reproducing kernels
and their biorthogonal: completeness or non-completeness?" by Anton
Baranov and Yurii Belov.
Abstract: Let $\{v_n\}$ be a complete minimal system in a Hilbert
space $\mathcal{H}$ and let $\{w_m\}$ be its biorthogonal system. It
is well known that $\{w_m\}$ is not necessarily complete. However the
situation may change if we consider systems of reproducing kernels in a
reproducing kernel Hilbert space $\mathcal{H}$ of analytic functions. We
study the completeness problem for a class of spaces with a Riesz basis
of reproducing kernels and for model subspaces $K_\Theta$ of the Hardy
space. We find a class of spaces where systems biorthogonal to complete
systems of reproducing kernels are always complete, and show that in
general this is not true. In particular we answer the question posed
by N.K. Nikolski and construct a model subspace with a non-complete
biorthogonal system.
Archive classification: math.CV math.FA
Mathematics Subject Classification: 30H05, 46E22, 30D50, 30D55, 47A15
Remarks: 28 pages
Submitted from: antonbaranov at netscape.net
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.1197
or
http://arXiv.org/abs/1005.1197
From alspach at fourier.math.okstate.edu Thu May 20 12:41:59 2010
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id 22F97D0D2E; Thu, 20 May 2010 12:41:59 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Veronica Dimant
Message-Id: <20100520174159.22F97D0D2E at fourier.math.okstate.edu>
Date: Thu, 20 May 2010 12:41:59 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "M-ideals of homogeneous
polynomials" by Veronica Dimant.
Abstract: We study the problem of whether $\mathcal{P}_w(^nE)$, the
space of $n$-homogeneous polynomials which are weakly continuous on
bounded sets, is an $M$-ideal in the space of continuous $n$-homogeneous
polynomials $\mathcal{P}(^nE)$. We obtain conditions that assure this
fact and present some examples. We prove that if $\mathcal{P}_w(^nE)$
is an $M$-ideal in $\mathcal{P}(^nE)$, then $\mathcal{P}_w(^nE)$
coincides with $\mathcal{P}_{w0}(^nE)$ ($n$-homogeneous
polynomials that are weakly continuous on bounded sets at 0). We
introduce a polynomial version of property $(M)$ and derive that if
$\mathcal{P}_w(^nE)=\mathcal{P}_{w0}(^nE)$ and $\mathcal{K}(E)$ is an
$M$-ideal in $\mathcal{L}(E)$, then $\mathcal{P}_w(^nE)$ is an $M$-ideal
in $\mathcal{P}(^nE)$. We also show that if $E^*$ has the approximation
property and $\mathcal{P}_w(^nE)$ is an $M$-ideal in $\mathcal{P}(^nE)$,
then the set of $n$-homogeneous polynomials whose Aron-Berner extension
do not attain the norm is nowhere dense in $\mathcal{P}(^nE)$. Finally,
we face an analogous $M$-ideal problem for block diagonal polynomials.
Archive classification: math.FA
Mathematics Subject Classification: 46G25, 46B04, 47L22, 46B20.
Submitted from: vero at udesa.edu.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.1260
or
http://arXiv.org/abs/1005.1260
From alspach at fourier.math.okstate.edu Thu Jun 3 15:04:50 2010
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id 8ADF1D0CC6; Thu, 3 Jun 2010 15:04:50 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Daniel A. Klain
Message-Id: <20100603200450.8ADF1D0CC6 at fourier.math.okstate.edu>
Date: Thu, 3 Jun 2010 15:04:50 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On the equality conditions of
the Brunn-Minkowski theorem" by Daniel A. Klain.
Abstract: This article describes a new proof of the equality condition
for the Brunn-Minkowski inequality.
Archive classification: math.MG math.CA math.FA
Mathematics Subject Classification: 52A20, 52A38, 52A39, 52A40
Remarks: 9 pages
Submitted from: daniel_klain at uml.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.1409
or
http://arXiv.org/abs/1005.1409
From alspach at fourier.math.okstate.edu Thu Jun 3 15:06:38 2010
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id 7198BD0CC6; Thu, 3 Jun 2010 15:06:38 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Manuel De la Rosa, Leonhard Frerick, Sophie Grivaux, and Alfredo Peris
Message-Id: <20100603200638.7198BD0CC6 at fourier.math.okstate.edu>
Date: Thu, 3 Jun 2010 15:06:38 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Frequent hypercyclicity, chaos,
and unconditional Schauder decompositions" by Manuel De la Rosa,
Leonhard Frerick, Sophie Grivaux, and Alfredo Peris.
Abstract: We prove that if X is any complex separable infinite-dimensional
Banach space with an unconditional Schauder decomposition, X supports
an operator T which is chaotic and frequently hypercyclic. This result
is extended to complex Frechet spaces with a continuous norm and an
unconditional Schauder decomposition, and also to complex Frechet spaces
with an unconditional basis, which gives a partial positive answer to
a problem posed by Bonet. We also solve a problem of Bes and Chan in
the negative by presenting hypercyclic, but non-chaotic operators on
\C^\N. We extend the main result to C_0-semigroups of operators. Finally,
in contrast with the complex case, we observe that there are real Banach
spaces with an unconditional basis which support no chaotic operator.
Archive classification: math.FA
Submitted from: grivaux at math.univ-lille1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.1416
or
http://arXiv.org/abs/1005.1416
From alspach at fourier.math.okstate.edu Thu Jun 3 15:07:54 2010
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id 72EF7D0CC6; Thu, 3 Jun 2010 15:07:54 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Alan D. Sokal
Message-Id: <20100603200754.72EF7D0CC6 at fourier.math.okstate.edu>
Date: Thu, 3 Jun 2010 15:07:54 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A really simple elementary proof
of the uniform boundedness theorem" by Alan D. Sokal.
Abstract: I give a proof of the uniform boundedness theorem that is
elementary (i.e. does not use any version of the Baire category theorem)
and also extremely simple.
Archive classification: math.FA
Mathematics Subject Classification: 46B99 (Primary), 46B20, 46B28
(Secondary)
Remarks: LaTex2e, 5 pages
Submitted from: sokal at nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.1585
or
http://arXiv.org/abs/1005.1585
From alspach at fourier.math.okstate.edu Thu Jun 3 15:09:14 2010
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To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Jordi Marzo and Kristian Seip
Message-Id: <20100603200914.CC097D0CC6 at fourier.math.okstate.edu>
Date: Thu, 3 Jun 2010 15:09:14 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "$L^\infty$ to $L^p$ constants
for Riesz projections" by Jordi Marzo and Kristian Seip.
Abstract: The norm of the Riesz projection from $L^\infty(\T^n)$ to
$L^p(\T^n)$ is considered. It is shown that for $n=1$, the norm equals
$1$ if and only if $p\le 4$ and that the norm behaves asymptotically
as $p/(\pi e)$ when $p\to \infty$. The critical exponent $p_n$ is the
supremum of those $p$ for which the norm equals $1$. It is proved that
$2+2/(2^n-1)\le p_n <4$ for $n>1$; it is unknown whether the critical
exponent for $n=\infty$ exceeds $2$.
Archive classification: math.FA math.CV
Mathematics Subject Classification: 41A44, 42B05, 46E30
Submitted from: seip at math.ntnu.no
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.1842
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http://arXiv.org/abs/1005.1842
From alspach at fourier.math.okstate.edu Thu Jun 3 15:17:06 2010
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id 86366D0CC6; Thu, 3 Jun 2010 15:17:06 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Pascal Lefevre, Daniel Li, Herve Queffelec, and Luis Rodriguez-Piazza
Message-Id: <20100603201706.86366D0CC6 at fourier.math.okstate.edu>
Date: Thu, 3 Jun 2010 15:17:06 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The canonical injection of the
Hardy-Orlicz space $H^\Psi$ into the Bergman-Orlicz space ${\mathfrak
B}^\Psi$" by Pascal Lefevre, Daniel Li, Herve Queffelec, and Luis
Rodriguez-Piazza.
Abstract: We study the canonical injection from the Hardy-Orlicz space
$H^\Psi$ into the Bergman-Orlicz space ${\mathfrak B}^\Psi$.
Archive classification: math.FA
Remarks: 21 pages
Submitted from: daniel.li at euler.univ-artois.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.1996
or
http://arXiv.org/abs/1005.1996
From alspach at fourier.math.okstate.edu Thu Jun 3 15:27:23 2010
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id 59981D0CC6; Thu, 3 Jun 2010 15:27:23 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Peter G. Casazza, Matt Fickus, Dustin Mixon and Janet C. Tremain
Message-Id: <20100603202723.59981D0CC6 at fourier.math.okstate.edu>
Date: Thu, 3 Jun 2010 15:27:23 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Concrete constructions of
non-pavable projections" by Peter G. Casazza, Matt Fickus, Dustin Mixon
and Janet C. Tremain.
Abstract: It is known that the paving conjecture fails for $2$-paving
projections with constant diagonal $1/2$. But the proofs of this fact are
existence proofs. We will give concrete examples of these projections
and projections with constant diagonal $1/r$ which are not $r$-pavable
in a very strong sense.
Archive classification: math.FA
Mathematics Subject Classification: 42C15, 46C05, 46C07
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/1005.2164
or
http://arXiv.org/abs/1005.2164
From alspach at fourier.math.okstate.edu Thu Jun 3 15:28:53 2010
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id EF9A8D0CC6; Thu, 3 Jun 2010 15:28:53 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Assaf Naor and Scott Sheffield
Message-Id: <20100603202853.EF9A8D0CC6 at fourier.math.okstate.edu>
Date: Thu, 3 Jun 2010 15:28:53 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Absolutely minimal Lipschitz
extension of tree-valued mappings" by Assaf Naor and Scott Sheffield.
Abstract: We prove that every Lipschitz function from a subset of a
locally compact length space to a metric tree has a unique absolutely
minimal Lipschitz extension (AMLE). We relate these extensions to a
stochastic game called {\bf Politics} --- a generalization of a game
called {\bf Tug of War} that has been used in~\cite{PSSW09} to study
real-valued AMLEs.
Archive classification: math.MG math.AP math.FA math.PR
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.2535
or
http://arXiv.org/abs/1005.2535
From alspach at fourier.math.okstate.edu Thu Jun 3 15:30:24 2010
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id 5C572D0CC6; Thu, 3 Jun 2010 15:30:24 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Daniel Carando and Daniel Galicer
Message-Id: <20100603203024.5C572D0CC6 at fourier.math.okstate.edu>
Date: Thu, 3 Jun 2010 15:30:24 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The symmetric Radon-Nikod\'ym
property for tensor norms" by Daniel Carando and Daniel Galicer.
Abstract: We introduce the symmetric-Radon-Nikod\'ym property (sRN
property) for finitely generated s-tensor norms $\beta$ of order
$n$ and prove a Lewis type theorem for s-tensor norms with this
property. As a consequence, if $\beta$ is a projective s-tensor
norm with the sRN property, then for every Asplund space $E$, the
canonical map $\widetilde{\otimes}_{ \beta }^{n,s} E' \rightarrow
\Big(\widetilde{\otimes}_{ \beta' }^{n,s} E \Big)'$ is a metric
surjection. This can be rephrased as the isometric isomorphism
$\mathcal{Q}^{min}(E) = \mathcal{Q}(E)$ for certain polynomial ideal
$\Q$. We also relate the sRN property of an s-tensor norm with the Asplund
or Radon-Nikod\'{y}m properties of different tensor products. Similar
results for full tensor products are also given. As an application,
results concerning the ideal of $n$-homogeneous extendible polynomials are
obtained, as well as a new proof of the well known isometric isomorphism
between nuclear and integral polynomials on Asplund spaces.
Archive classification: math.FA
Mathematics Subject Classification: 47L22, 46M05, 46B22
Remarks: 17 pages
Submitted from: dgalicer at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.2683
or
http://arXiv.org/abs/1005.2683
From alspach at fourier.math.okstate.edu Thu Jun 3 15:32:03 2010
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id 8E5B8D0CC6; Thu, 3 Jun 2010 15:32:03 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Jarno Talponen
Message-Id: <20100603203203.8E5B8D0CC6 at fourier.math.okstate.edu>
Date: Thu, 3 Jun 2010 15:32:03 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Directionally Euclidean structures
of Banach spaces" by Jarno Talponen.
Abstract: We study spaces with directionally asymptotically controlled
ellipsoids approximating the unit ball in finite-dimensions. These
ellipsoids are the unique minimum volume ellipsoids, which contain
the unit ball of the corresponding finite-dimensional subspace. The
directional control here means that we evaluate the ellipsoids with a
given functional of the dual space. The term asymptotical refers to the
fact that we take '$\limsup$' over finite-dimensional subspaces.
This leads to some isomorphic and isometric characterizations of Hilbert
spaces. An application involving Mazur's rotation problem is given. We
also discuss the complexity of the family of ellipsoids as the dimension
and geometry vary.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46C15, Secondary 52A23
Remarks: 10 pages
Submitted from: talponen at cc.hut.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.2737
or
http://arXiv.org/abs/1005.2737
From alspach at fourier.math.okstate.edu Thu Jun 3 15:34:33 2010
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id 60926D0CC6; Thu, 3 Jun 2010 15:34:33 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Tommi Hoynalanmaa
Message-Id: <20100603203433.60926D0CC6 at fourier.math.okstate.edu>
Date: Thu, 3 Jun 2010 15:34:33 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Multiresolution analysis for
compactly supported interpolating tensor product wavelets" by Tommi
Hoynalanmaa.
Abstract: We construct a one-dimensional interpolating multiresolution
analysis (MRA) of C0(R,K), K = R or K = C, and multidimensional
interpolating tensor product MRAs of the function spaces C0(Rn,K)
consisting of real or complex valued functions on Rn vanishing at infinity
and the function spaces Cu(Rn,K) consisting of bounded and uniformly
continuous functions on Rn. The theory of the tensor products of Banach
spaces is used. We also generalize the Besov space norm equivalence
result from Donoho (1992, Interpolating Wavelet Transforms) for our
n-dimensional construction.
Archive classification: math.FA
Mathematics Subject Classification: 46A32 (Primary), 46B28 (Secondary),
15A69 (Secondary), 46E10
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.3371
or
http://arXiv.org/abs/1005.3371
From alspach at fourier.math.okstate.edu Thu Jun 3 15:35:55 2010
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id D1909D0CC6; Thu, 3 Jun 2010 15:35:55 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Christina Brech
Message-Id: <20100603203555.D1909D0CC6 at fourier.math.okstate.edu>
Date: Thu, 3 Jun 2010 15:35:55 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On the density of Banach {$C(K)$}
spaces with the Grothendieck property" by Christina Brech.
Abstract: Using the method of forcing we prove that consistently
there is a Banach space of continuous functions on a compact Hausdorff
space with the Grothendieck property and with density less than the
continuum. It follows that the classical result stating that ``no
nontrivial complemented subspace of a Grothendieck $C(K)$ space is
separable'' cannot be strengthened by replacing ``is separable'' by
``has density less than that of $l_\infty$'', without using an additional
set-theoretic assumption. Such a strengthening was proved by Haydon,
Levy and Odell, assuming Martin's axiom and the negation of the continuum
hypothesis. Moreover, our example shows that certain separation properties
of Boolean algebras are quite far from the Grothendieck property.
Archive classification: math.FA
Citation: Proc. Amer. Math. Soc. 134, No. 12, 3653-3663 (2006)
Submitted from: christina.brech at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.3524
or
http://arXiv.org/abs/1005.3524
From alspach at fourier.math.okstate.edu Thu Jun 3 15:38:23 2010
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id 9E9DDD0CC6; Thu, 3 Jun 2010 15:38:23 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Christina Brech and Piotr Koszmider
Message-Id: <20100603203823.9E9DDD0CC6 at fourier.math.okstate.edu>
Date: Thu, 3 Jun 2010 15:38:23 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Thin-very tall compact scattered
spaces which are hereditarily separable" by Christina Brech and Piotr
Koszmider.
Abstract: We strengthen the property $\Delta$ of a function
$f:[\omega_2]^2\rightarrow [\omega_2]^{\leq \omega}$ considered
by Baumgartner and Shelah. This allows us to consider new types of
amalgamations in the forcing used by Rabus, Juh\'asz and Soukup to
construct thin-very tall compact scattered spaces. We consistently
obtain spaces $K$ as above where $K^n$ is hereditarily separable for each
$n\in\N$. This serves as a counterexample concerning cardinal functions
on compact spaces as well as having some applications in Banach spaces:
the Banach space $C(K)$ is an Asplund space of density $\aleph_2$ which
has no Fr\'echet smooth renorming, nor an uncountable biorthogonal system.
Archive classification: math.FA math.GN
Remarks: accepted to Trans. Amer. Math. Soc.
Submitted from: christina.brech at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.3528
or
http://arXiv.org/abs/1005.3528
From alspach at fourier.math.okstate.edu Thu Jun 3 15:39:37 2010
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id 5A56CD0CC6; Thu, 3 Jun 2010 15:39:37 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Christina Brech and Piotr Koszmider
Message-Id: <20100603203937.5A56CD0CC6 at fourier.math.okstate.edu>
Date: Thu, 3 Jun 2010 15:39:37 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On universal Banach spaces of
density continuum" by Christina Brech and Piotr Koszmider.
Abstract: We consider the question whether there exists a Banach space $X$
of density continuum such that every Banach space of density not bigger
than continuum isomorphically embeds into $X$ (called a universal Banach
space of density $\cc$). It is well known that $\ell_\infty/c_0$ is such
a space if we assume the continuum hypothesis. However, some additional
set-theoretic assumption is needed, as we prove in the main result of
this paper that it is consistent with the usual axioms of set-theory
that there is no universal Banach space of density $\cc$. Thus, the
problem of the existence of a universal Banach space of density $\cc$
is undecidable using the usual axioms of set-theory.
We also prove that it is consistent that there are universal Banach
spaces of density $\cc$, but $\ell_\infty/c_0$ is not among them. This
relies on the proof of the consistency of the nonexistence of an
isomorphic embedding of $C([0,\cc])$ into $\ell_\infty/c_0$.
Archive classification: math.FA
Submitted from: christina.brech at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.3530
or
http://arXiv.org/abs/1005.3530
From alspach at fourier.math.okstate.edu Thu Jun 3 15:40:47 2010
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id 86A2FD0CC6; Thu, 3 Jun 2010 15:40:47 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Christina Brech and Piotr Koszmider
Message-Id: <20100603204047.86A2FD0CC6 at fourier.math.okstate.edu>
Date: Thu, 3 Jun 2010 15:40:47 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On biorthogonal systems whose
functionals are finitely supported" by Christina Brech and Piotr
Koszmider.
Abstract: We show that for each natural $n>1$ it is consistent that there
is a compact Hausdorff space $K_{2n}$ such that in $C(K_{2n})$ there
is no uncountable (semi)biorthogonal sequence $(f_\xi,\mu_\xi)_{\xi\in
\omega_1}$ where $\mu_\xi$'s are atomic measures with supports consisting
of at most $2n-1$ points of $K_{2n}$, but there are biorthogonal systems
$(f_\xi,\mu_\xi)_{\xi\in \omega_1}$ where $\mu_\xi$'s are atomic measures
with supports consisting of $2n$ points. This complements a result of
Todorcevic that it is consistent that each nonseparable Banach space
$C(K)$ has an uncountable biorthogonal system where the functionals are
measures of the form $\delta_{x_\xi}-\delta_{y_\xi}$ for $\xi<\omega_1$
and $x_\xi,y_\xi\in K$. It also follows that it is consistent that the
irredundance of the Boolean algebra $Clop(K)$ or the Banach algebra
$C(K)$ for $K$ totally disconnected can be strictly smaller than the
sizes of biorthogonal systems in $C(K)$. The compact spaces exhibit an
interesting behaviour with respect to known cardinal functions: the
hereditary density of the powers $K_{2n}^k$ is countable up to $k=n$
and it is uncountable (even the spread is uncountable) for $k>n$.
Archive classification: math.FA
Submitted from: christina.brech at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.3532
or
http://arXiv.org/abs/1005.3532
From alspach at fourier.math.okstate.edu Mon Jun 7 11:30:50 2010
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id F0485D0CDF; Mon, 7 Jun 2010 11:30:49 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by T. Bermudez, A. bonilla, F. Martinez-Gimenez, and A. Peris
Message-Id: <20100607163049.F0485D0CDF at fourier.math.okstate.edu>
Date: Mon, 7 Jun 2010 11:30:49 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Li-Yorke and distributionally
chaotic operators" by T. Bermudez, A. bonilla, F. Martinez-Gimenez,
and A. Peris.
Abstract: We study Li-Yorke chaos and distributional chaos for operators
on Banach spaces. More precisely, we characterize Li-Yorke chaos in
terms of the existence of irregular vectors. Sufficient ``computable''
criteria for distributional and Li-Yorke chaos are given, together with
the existence of dense scrambled sets under some additional conditions. We
also obtain certain spectral properties. Finally, we show that every
infinite dimensional separable Banach space admits a distributionally
chaotic operator which is also hypercyclic.
Archive classification: math.FA
Mathematics Subject Classification: 47A16
Submitted from: tbermude at ull.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.3634
or
http://arXiv.org/abs/1005.3634
From alspach at fourier.math.okstate.edu Mon Jun 7 11:32:26 2010
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id A6997D0CDF; Mon, 7 Jun 2010 11:32:26 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Antonio Aviles and Ondrej F.K. Kalenda
Message-Id: <20100607163226.A6997D0CDF at fourier.math.okstate.edu>
Date: Mon, 7 Jun 2010 11:32:26 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Compactness in Banach space theory
- selected problems" by Antonio Aviles and Ondrej F.K. Kalenda.
Abstract: We list a number of problems in several topics related to
compactness in nonseparable Banach spaces. Namely, about the Hilbertian
ball in its weak topology, spaces of continuous functions on Eberlein
compacta, WCG Banach spaces, Valdivia compacta and Radon-Nikod\'{y}m
compacta.
Archive classification: math.FA math.GN
Submitted from: kalenda at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.4303
or
http://arXiv.org/abs/1005.4303
From alspach at fourier.math.okstate.edu Mon Jun 7 11:34:15 2010
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id 69880D0CDF; Mon, 7 Jun 2010 11:34:15 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Bernardo Cascales, Ondrej F.K. Kalenda and Jiri Spurny
Message-Id: <20100607163415.69880D0CDF at fourier.math.okstate.edu>
Date: Mon, 7 Jun 2010 11:34:15 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A quantitative version of James'
compactness theorem" by Bernardo Cascales, Ondrej F.K. Kalenda and
Jiri Spurny.
Abstract: We introduce two measures of weak non-compactness $Ja_E$ and
$Ja$ that quantify, via distances, the idea of boundary behind James'
compactness theorem. These measures tell us, for a bounded subset $C$ of
a Banach space $E$ and for given $x^*\in E^*$, how far from $E$ or $C$
one needs to go to find $x^{**}\in \overline{C}^{w^*}\subset E^{**}$
with $x^{**}(x^*)=\sup x^* (C)$. A quantitative version of James'
compactness theorem is proved using $Ja_E$ and $Ja$, and in particular
it yields the following result: {\it Let $C$ be a closed convex bounded
subset of a Banach space $E$ and $r>0$. If there is an element $x_0^{**}$
in $\overline{C}^{w^*}$ whose distance to $C$ is greater than $r$, then
there is $x^*\in E^*$ such that each $x^{**}\in\overline{C}^{w^*}$ at
which $\sup x^*(C)$ is attained has distance to $E$ greater than $r/2$.}
We indeed establish that $Ja_E$ and $Ja$ are equivalent to other measures
of weak non-compactness studied in the literature. We also collect
particular cases and examples showing when the inequalities between the
different measures of weak non-compactness can be equalities and when
the inequalities are sharp.
Archive classification: math.FA
Remarks: 16 pages
Submitted from: kalenda at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.5693
or
http://arXiv.org/abs/1005.5693
From alspach at fourier.math.okstate.edu Mon Jun 7 11:35:27 2010
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id 499E7D0CDF; Mon, 7 Jun 2010 11:35:27 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Turdebek N. Bekjan, Zeqian Chen, and Peide Liu
Message-Id: <20100607163527.499E7D0CDF at fourier.math.okstate.edu>
Date: Mon, 7 Jun 2010 11:35:27 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Noncommutative weak Orlicz spaces
and martingale inequalities" by Turdebek N. Bekjan, Zeqian Chen, and
Peide Liu.
Abstract: This paper is devoted to the study of noncommutative weak
Orlicz spaces. Marcinkiewicz interpolation theorem is extended to
include noncommutative weak Orlicz spaces as interpolation classes. In
particular, we prove the Burkholder-Gundy inequality in the setting of
noncommutative weak Orlicz spaces.
Archive classification: math.FA
Remarks: 26 pages
Submitted from: zqchen at wipm.ac.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.0091
or
http://arXiv.org/abs/1006.0091
From alspach at fourier.math.okstate.edu Mon Jun 7 11:40:57 2010
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id A1144D0CDF; Mon, 7 Jun 2010 11:40:57 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Daniel Pellegrino
Message-Id: <20100607164057.A1144D0CDF at fourier.math.okstate.edu>
Date: Mon, 7 Jun 2010 11:40:57 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "An inclusion principle for general
classes of nonlinear absolutely summing maps" by Daniel Pellegrino.
Abstract: The inclusion theorem for absolutely summing linear operators
asserts that under certain assumptions on $p_{1},p_{2},q_{1}$ and
$q_{2},$ every absolutely $(q_{1},p_{1})$-summing linear operator is
also absolutely $(q_{2},p_{2}% )$-summing. In this note we obtain some
variants of this result in a completely nonlinear setting.
Archive classification: math.FA
Remarks: 11 pages
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.0536
or
http://arXiv.org/abs/1006.0536
From alspach at fourier.math.okstate.edu Mon Jun 7 11:43:36 2010
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id 6E292D0CDF; Mon, 7 Jun 2010 11:43:36 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Daniel Pellegrino and Joedson Santos
Message-Id: <20100607164336.6E292D0CDF at fourier.math.okstate.edu>
Date: Mon, 7 Jun 2010 11:43:36 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper 'A remark on the paper "A Unified
Pietsch Domination Theorem"' by Daniel Pellegrino and Joedson Santos.
Abstract: In this short communication we show that the Unified Pietsch
Domination proved by Botelho et al in a recent paper remains true even
if we remove two of its apparently crucial hypothesis.
Archive classification: math.FA
Remarks: 3 pages
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.0753
or
http://arXiv.org/abs/1006.0753
From alspach at fourier.math.okstate.edu Mon Jun 7 11:45:05 2010
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id 56EAAD0CDF; Mon, 7 Jun 2010 11:45:05 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by S.A. Argyros, V. Kanellopoulos, and K. Tyros
Message-Id: <20100607164505.56EAAD0CDF at fourier.math.okstate.edu>
Date: Mon, 7 Jun 2010 11:45:05 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Spreading models in Banach space
theory" by S.A. Argyros, V. Kanellopoulos, and K. Tyros.
Abstract: We extend the classical Brunel-Sucheston definition of
the spreading model by introducing the $\mathcal{F}$-sequences
$(x_s)_{s\in\mathcal{F}}$ in a Banach space and the plegma families
in $\mathcal{F}$ where $\mathcal{F}$ is a regular thin family. The
new concept yields a transfinite increasing hierarchy of classes of
1-subsymmetric sequences. We explore the corresponding theory and
we present examples establishing this hierarchy and illustrating the
limitation of the theory.
Archive classification: math.FA math.CO
Remarks: vi+115 pages
Submitted from: ktyros at central.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.0957
or
http://arXiv.org/abs/1006.0957
From banach-bounces at math.okstate.edu Thu Jul 1 13:41:25 2010
Return-Path: <alspach at fourier.math.okstate.edu>
Subject: SUMIRFAS 2010
Date: Thu, 1 Jul 2010 13:28:26 -0500 (CDT)
From: Bill Johnson <johnson at math.tamu.edu>
To: banach at math.okstate.edu
1st ANNOUNCEMENT OF SUMIRFAS 2010
The Informal Regional Functional Analysis Seminar
July 30 - August 1
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/conferences/linanalysis/
The first talk will be in the early afternoon on Friday and the Seminar
concludes by lunch time on Sunday. All talks will be in Blocker 169. The
Blocker Building is on Ireland St. just south of University Dr. on the
Texas A&M campus:
http://www.tamu.edu/map/building/overview/BLOC.html.
Coffee and refreshments will be available in Blocker 148.
Speakers at SUMIRFAS 2010 include
Florent Baudier, On various geometric properties of metric spaces
Ionut Chifan, Von Neumann algebras with unique group measure space Cartan
subalgebras
Ken Davidson, Nevanlinna-Pick interpolation and factorization of
functionals
Quanlei Fang, Commutators and localization on the Drury-Arveson space
Kevin Beanland, Strictly singular operators between separable Banach
spaces
Ted Gamelin, Composition operators on uniform algebras
Assaf Naor, Towards a calculus for non-linear spectral gaps
Roger Smith, Close nuclear separable C$^*$-algebras
Nicole Tomczak-Jaegermann, On random matrices with independent log-concave
columns
Joel A. Tropp, User-friendly tail bounds for sums of random matrices
Michael Anshelevich (chair), Jinho Baik, and Roland Speicher are
organizing
a Concentration Week on "Orthogonal Polynomials in Probability Theory" for
the week of July 6-10. The theme of this Concentration Week is orthogonal
polynomial techniques in probability theory, especially in the study of
random matrices, free probability, and multiple stochastic integrals. Baik
and Speicher will give mini-courses designed to introduce non specialists
to these topics. The home page for this Concentration Week is at
http://www.math.tamu.edu/~manshel/OPPT/main.html
Ilijas Farah and David Kerr (chair) are organizing a Concentration Week
on "Set Theory and Functional Analysis" for the week of July 26-30. The
broad theme will be recent applications of set theory in functional
analysis, with emphasis on combinatorial phenomena and classifiability
problems in operator algebras, dynamics, and Banach space theory. The
program will include lecture series by Christian Rosendal, David Sherman,
and Todor Tsankov. The home page for this Concentration Week is at
http://www.math.tamu.edu/~kerr/concweek10/index.html
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 her if
you are requesting support. Minorities, women, graduate students, and
young
researchers are especially encouraged to apply.
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, contact Cara
Barton <cara at math.tamu.edu>. For more information on the Workshop itself,
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 "Orthogonal Polynomials in
Probability Theory", contact Michael Anshelevich <manshel at math.tamu.edu>.
For information about the Concentration Week "Set Theory and Functional
Analysis", contact David Kerr <kerr at math.tamu.edu>.
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Sun Jul 4 11:23:04 2010
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id 6C728D08F0; Sun, 4 Jul 2010 11:23:04 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by F. Dadipour and M. S. Moslehian
Message-Id: <20100704162304.6C728D08F0 at fourier.math.okstate.edu>
Date: Sun, 4 Jul 2010 11:23:04 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A characterization of inner
product spaces related to the p-angular distance" by F. Dadipour and
M. S. Moslehian.
Abstract: In this paper we present a new characterization of inner product
spaces related to the p-angular distance. We also generalize some results
due to Dunkl, Williams, Kirk, Smiley and Al-Rashed by using the notion
of p-angular distance.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46C15, Secondary 46B20, 46C05
Remarks: 9 Pages, to appear in J. Math. Anal. Appl. (JMAA)
Submitted from: moslehian at ferdowsi.um.ac.ir
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.1022
or
http://arXiv.org/abs/1006.1022
From alspach at fourier.math.okstate.edu Sun Jul 4 11:25:18 2010
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id 48206D08F0; Sun, 4 Jul 2010 11:25:18 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Konrad J. Swanepoel
Message-Id: <20100704162518.48206D08F0 at fourier.math.okstate.edu>
Date: Sun, 4 Jul 2010 11:25:18 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Sets of unit vectors with small
pairwise sums" by Konrad J. Swanepoel.
Abstract: We study the sizes of delta-additive sets of unit vectors
in a d-dimensional normed space: the sum of any two vectors has norm
at most delta. One-additive sets originate in finding upper bounds of
vertex degrees of Steiner Minimum Trees in finite dimensional smooth
normed spaces (Z. F\"uredi, J. C. Lagarias, F. Morgan, 1991). We show
that the maximum size of a delta-additive set over all normed spaces
of dimension d grows exponentially in d for fixed delta>2/3, stays
bounded for delta<2/3, and grows linearly at the threshold delta=2/3.
Furthermore, the maximum size of a 2/3-additive set in d-dimensional
normed space has the sharp upper bound of d, with the single exception
of spaces isometric to three-dimensional l^1 space, where there exists
a 2/3-additive set of four unit vectors.
Archive classification: math.MG math.FA
Mathematics Subject Classification: Primary 46B20. Secondary 52A21, 52B10
Citation: Quaestiones Mathematicae 23 (2000) 383-388
Remarks: 6 pages. Old paper of 10 years ago
Submitted from: konrad.swanepoel at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.1051
or
http://arXiv.org/abs/1006.1051
From alspach at fourier.math.okstate.edu Sun Jul 4 11:55:39 2010
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id DCAAAD08F0; Sun, 4 Jul 2010 11:55:39 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Geraldo Botelho, Erhan Caliskan and Daniel Pellegrino
Message-Id: <20100704165539.DCAAAD08F0 at fourier.math.okstate.edu>
Date: Sun, 4 Jul 2010 11:55:39 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On the representation of
multi-ideals by tensor norms" by Geraldo Botelho, Erhan Caliskan and
Daniel Pellegrino.
Abstract: A tensor norm
isomorphism. In this paper we study the representation of multi-ideals
and of ideals of multilinear forms by smooth tensor norms
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.1540
or
http://arXiv.org/abs/1006.1540
From alspach at fourier.math.okstate.edu Sun Jul 4 11:57:09 2010
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X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id B022FD08F0; Sun, 4 Jul 2010 11:57:09 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Jaegil Kim, Vladyslav Yaskin and Artem Zvavitch
Message-Id: <20100704165709.B022FD08F0 at fourier.math.okstate.edu>
Date: Sun, 4 Jul 2010 11:57:09 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The geometry of p-convex
intersection bodies" by Jaegil Kim, Vladyslav Yaskin and Artem Zvavitch.
Abstract: Busemann's theorem states that the intersection body of an
origin-symmetric convex body is also convex. In this paper we provide
a version of Busemann's theorem for p-convex bodies. We show that
the intersection body of a p-convex body is q-convex for certain
q. Furthermore, we discuss the sharpness of the previous result by
constructing an appropriate example. This example is also used to show
that IK, the intersection body of K, can be much farther away from the
Euclidean ball than K. Finally, we extend these theorems to some general
measure spaces with log-concave and $s$-concave measures
Archive classification: math.FA
Mathematics Subject Classification: 44A12, 52A15, 52A21
Submitted from: zvavitch at math.kent.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.1546
or
http://arXiv.org/abs/1006.1546
From alspach at fourier.math.okstate.edu Sun Jul 4 11:58:34 2010
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id 87A12D08F0; Sun, 4 Jul 2010 11:58:34 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Catalin Badea and Yuri I. Lyubich
Message-Id: <20100704165834.87A12D08F0 at fourier.math.okstate.edu>
Date: Sun, 4 Jul 2010 11:58:34 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Geometric, spectral and asymptotic
properties of averaged products of projections in Banach spaces"
by Catalin Badea and Yuri I. Lyubich.
Abstract: According to the von Neumann-Halperin and Lapidus theorems,
in a Hilbert space the iterates of products or, respectively, of convex
combinations of orthoprojections are strongly convergent. We extend
these results to the iterates of convex combinations of products of some
projections in a complex Banach space. The latter is assumed uniformly
convex or uniformly smooth for the orthoprojections, or reflexive for
more special projections, in particular, for the hermitian ones. In all
cases the proof of convergence is based on a known criterion in terms
of the boundary spectrum.
Archive classification: math.FA
Remarks: 22 pages
Submitted from: catalin.badea at math.univ-lille1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.2052
or
http://arXiv.org/abs/1006.2052
From alspach at fourier.math.okstate.edu Sun Jul 4 11:59:59 2010
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id A2D1DD08F0; Sun, 4 Jul 2010 11:59:59 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Catalin Badea, Sophie Grivaux and Vladimir Muller
Message-Id: <20100704165959.A2D1DD08F0 at fourier.math.okstate.edu>
Date: Sun, 4 Jul 2010 11:59:59 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The rate of convergence in the
method of alternating projections" by Catalin Badea, Sophie Grivaux and
Vladimir Muller.
Abstract: A generalization of the cosine of the Friedrichs angle between
two subspaces to a parameter associated to several closed subspaces of
a Hilbert space is given. This parameter is used to analyze the rate of
convergence in the von Neumann-Halperin method of cyclic alternating
projections. General dichotomy theorems are proved, in the Hilbert or
Banach space situation, providing conditions under which the alternative
QUC/ASC (quick uniform convergence versus arbitrarily slow convergence)
holds. Several meanings for ASC are proposed.
Archive classification: math.FA math.NA
Remarks: 23 pages, to appear in St. Petersburg Math J. (2010)
Submitted from: catalin.badea at math.univ-lille1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.2047
or
http://arXiv.org/abs/1006.2047
From alspach at fourier.math.okstate.edu
Return-path: <banach-bounces at math.okstate.edu>
Subject: [Banach] New Journal - Annals of Functional Analysis
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 06 Jul 2010 10:29:39 -0500
To: banach at math.okstate.edu
Dear colleague,
It is my pleasure to invite you to submit a research paper of high
standard or critical survey paper for possible publication in the
electronic journal.
"Annals of Functional Analysis (AFA)"
http://www.emis.de/journals/AFA/
It would be appreciated if you promote the journal among your
fellow-workers and colleagues.
Best wishes
M. S. Moslehian
Editor-in-chief of AFA
**********************************************
Mohammad Sal Moslehian
Ph.D., Professor of Mathematics
Address: Dept. of Pure Math., P.O. Box 1159
Ferdowsi University of Mashhad
Mashhad 91775, Iran
Mobile: (+98)(9151140894)
Tel-Fax: (+98)(511)(8828606)
E-mails: moslehian at ams.org
moslehian at um.ac.ir
Home: http://www.um.ac.ir/~moslehian/
**********************************************
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Tue Jul 6 16:03:46 2010
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id C5611D0B17; Tue, 6 Jul 2010 16:03:46 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Pandelis Dodos
Message-Id: <20100706210346.C5611D0B17 at fourier.math.okstate.edu>
Date: Tue, 6 Jul 2010 16:03:46 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Quotients of Banach spaces and
surjectively universal spaces" by Pandelis Dodos.
Abstract: We characterize those classes $\mathcal{C}$ of separable
Banach spaces for which there exists a separable Banach space $Y$ not
containing $\ell_1$ and such that every space in the class $\mathcal{C}$
is a quotient of $Y$.
Archive classification: math.FA
Citation: Studia Mathematica 197 (2010), 171-194
Remarks: 23 pages, no figures
Submitted from: pdodos at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.2665
or
http://arXiv.org/abs/1006.2665
From alspach at fourier.math.okstate.edu Tue Jul 6 16:06:08 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 117AAD0B17; Tue, 6 Jul 2010 16:06:07 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Kevin Benaland and Pandelis Dodos
Message-Id: <20100706210608.117AAD0B17 at fourier.math.okstate.edu>
Date: Tue, 6 Jul 2010 16:06:08 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On strictly singular operators
between separable Banach spaces" by Kevin Beanland and Pandelis Dodos.
Abstract: Let $X$ and $Y$ be separable Banach spaces and denote
by $\sss\sss(X,Y)$ the subset of $\llll(X,Y)$ consisting of all
strictly singular operators. We study various ordinal ranks on the set
$\sss\sss(X,Y)$. Our main results are summarized as follows. Firstly,
we define a new rank $\rs$ on $\sss\sss(X,Y)$. We show that $\rs$ is
a co-analytic rank and that dominates the rank $\varrho$ introduced by
Androulakis, Dodos, Sirotkin and Troitsky [Israel J. Math., 169 (2009),
221-250]. Secondly, for every $1\leq p<+\infty$ we construct a Banach
space $Y_p$ with an unconditional basis such that $\sss\sss(\ell_p,
Y_p)$ is a co-analytic non-Borel subset of $\llll(\ell_p,Y_p)$ yet every
strictly singular operator $T:\ell_p\to Y_p$ satisfies $\varrho(T)\leq
2$. This answers a question of Argyros.
Archive classification: math.FA
Remarks: 20 pages, no figures; Mathematika, to appear
Submitted from: pdodos at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.2672
or
http://arXiv.org/abs/1006.2672
From alspach at fourier.math.okstate.edu Tue Jul 6 16:08:32 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
Delivered-To: alspach at fourier.math.okstate.edu
Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id BD28BD0B17; Tue, 6 Jul 2010 16:08:32 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Pandelis Dodos
Message-Id: <20100706210832.BD28BD0B17 at fourier.math.okstate.edu>
Date: Tue, 6 Jul 2010 16:08:32 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Operators whose dual has
non-separable range" by Pandelis Dodos.
Abstract: Let $X$ and $Y$ be separable Banach spaces and $T:X\to Y$
be a bounded linear operator. We characterize the non-separability of
$T^*(Y^*)$ by means of fixing properties of the operator $T$.
Archive classification: math.FA
Remarks: 20 pages, no figures
Submitted from: pdodos at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.2666
or
http://arXiv.org/abs/1006.2666
From alspach at fourier.math.okstate.edu Tue Jul 6 16:09:57 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 7DE77D0B17; Tue, 6 Jul 2010 16:09:57 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Pandelis Dodos, Jordi Lopez-Abad and Stevo Todorcevic
Message-Id: <20100706210957.7DE77D0B17 at fourier.math.okstate.edu>
Date: Tue, 6 Jul 2010 16:09:57 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Banach spaces and Ramsey theory:
some open problems" by Pandelis Dodos, Jordi Lopez-Abad and Stevo
Todorcevic.
Abstract: We discuss some open problems in the Geometry of Banach spaces
having Ramsey-theoretic flavor. The problems are exposed together with
well known results related to them.
Archive classification: math.FA math.CO
Remarks: 17 pages, no figures; RACSAM, to appear
Submitted from: pdodos at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.2668
or
http://arXiv.org/abs/1006.2668
From alspach at fourier.math.okstate.edu Wed Jul 14 12:24:59 2010
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id 6C387D0B3A; Wed, 14 Jul 2010 12:24:59 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Sergey Bobkov, Mokshay Madiman, and Liyao Wang
Message-Id: <20100714172459.6C387D0B3A at fourier.math.okstate.edu>
Date: Wed, 14 Jul 2010 12:24:59 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Fractional generalizations of
Young and Brunn-Minkowski inequalities" by Sergey Bobkov, Mokshay Madiman,
and Liyao Wang.
Abstract: A generalization of Young's inequality for convolution
with sharp constant is conjectured for scenarios where more than two
functions are being convolved, and it is proven for certain parameter
ranges. The conjecture would provide a unified proof of recent entropy
power inequalities of Barron and Madiman, as well as of a (conjectured)
generalization of the Brunn-Minkowski inequality. It is shown that
the generalized Brunn-Minkowski conjecture is true for convex sets;
an application of this to the law of large numbers for random sets
is described.
Archive classification: math.FA cs.IT math.IT math.PR
Remarks: 17 pages
Submitted from: mokshay.madiman at yale.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.2884
or
http://arXiv.org/abs/1006.2884
From alspach at fourier.math.okstate.edu Wed Jul 14 12:26:53 2010
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id 8AFE2D0B3A; Wed, 14 Jul 2010 12:26:53 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Jesus Araujo and Luis Dubarbie
Message-Id: <20100714172653.8AFE2D0B3A at fourier.math.okstate.edu>
Date: Wed, 14 Jul 2010 12:26:53 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Noncompactness and noncompleteness
in isometries of Lipschitz spaces" by Jesus Araujo and Luis Dubarbie.
Abstract: We solve the following two questions concerning
surjective linear isometries between spaces of Lipschitz functions
$\mathrm{Lip}(X,E)$ and $\mathrm{Lip}(Y,F)$, for strictly convex normed
spaces $E$ and $F$ and metric spaces $X$ and $Y$:
\begin{enumerate} \item Characterize those base spaces $X$ and $Y$
for which all isometries are
weighted composition maps.
\item Give a condition independent of base spaces under which all
isometries
are weighted composition maps.
\end{enumerate} In particular, we prove that requirements of
completeness on $X$ and $Y$ are
not necessary when $E$ and $F$ are not complete, which is in sharp
contrast with results known in the scalar context. We also give the
special form of this kind of isometries.
Archive classification: math.FA
Mathematics Subject Classification: 2010: 47B33 (Primary), 46B04, 46E15,
46E40, 47B38 (Secondary)
Remarks: 14 pages, no figures, \documentclass[12pt]{amsart}
Submitted from: araujoj at unican.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.2995
or
http://arXiv.org/abs/1006.2995
From alspach at fourier.math.okstate.edu Wed Jul 14 12:29:42 2010
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id 5FA36D0B3A; Wed, 14 Jul 2010 12:29:42 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Iryna Banakh and Taras Banakh
Message-Id: <20100714172942.5FA36D0B3A at fourier.math.okstate.edu>
Date: Wed, 14 Jul 2010 12:29:42 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Constructing non-compact operators
into $c_0$" by Iryna Banakh and Taras Banakh.
Abstract: We prove that for each dense non-compact linear operator
$S:X\to Y$ between Banach spaces there is a linear operator $T:Y\to c_0$
such that the operator $TS:X\to c_0$ is not compact. This generalizes
the Josefson-Nissenzweig Theorem.
Archive classification: math.FA
Mathematics Subject Classification: 47B07, 46B15
Remarks: 2 pages
Submitted from: tbanakh at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.3089
or
http://arXiv.org/abs/1006.3089
From alspach at fourier.math.okstate.edu Wed Jul 14 12:31:15 2010
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id EADE5D0B3A; Wed, 14 Jul 2010 12:31:15 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Taras Banakh and Robert Cauty
Message-Id: <20100714173115.EADE5D0B3A at fourier.math.okstate.edu>
Date: Wed, 14 Jul 2010 12:31:15 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Topological classification of
closed convex sets in Frechet spaces" by Taras Banakh and Robert Cauty.
Abstract: We prove that each non-separable completely metrizable convex
subset of a Frechet space is homeomorphic to a Hilbert space. This
resolves an old (more than 30 years) problem of infinite-dimensional
topology. Combined with the topological classification of separable convex
sets due to Klee, Dobrowoslki and Torunczyk, this result implies that each
closed convex subset of a Frechet space is homemorphic to $[0,1]^n\times
[0,1)^m\times l_2(k)$ for some cardinals $0\le n\le\omega$, $0\le m\le 1$
and $k\ge 0$.
Archive classification: math.FA math.GN math.GT
Mathematics Subject Classification: 57N17, 46A04
Remarks: 8 pages
Submitted from: tbanakh at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.3092
or
http://arXiv.org/abs/1006.3092
From alspach at fourier.math.okstate.edu Wed Jul 14 12:32:54 2010
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id 0D3C4D0B3A; Wed, 14 Jul 2010 12:32:53 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Mikhail Lifshits and Werner Linde
Message-Id: <20100714173254.0D3C4D0B3A at fourier.math.okstate.edu>
Date: Wed, 14 Jul 2010 12:32:53 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Compactness properties of weighted
summation operators on trees" by Mikhail Lifshits and Werner Linde.
Abstract: We investigate compactness properties of weighted summation
operators $V_{\alpha,\sigma}$ as mapping from $\ell_1(T)$ into
$\ell_q(T)$ for some $q\in (1,\infty)$. Those operators are defined
by $$ (V_{\alpha,\sigma} x)(t) :=\alpha(t)\sum_{s\succeq t}\sigma(s)
x(s)\,,\quad t\in T\;, $$ where $T$ is a tree with induced partial
order $t \preceq s$ (or $s \succeq t$) for $t,s\in T$. Here $\alpha$
and $\sigma$ are given weights on $T$. We introduce a metric $d$
on $T$ such that compactness properties of $(T,d)$ imply two--sided
estimates for $e_n(V_{\alpha,\sigma})$, the (dyadic) entropy numbers
of $V_{\alpha,\sigma}$. The results are applied for concrete trees as
e.g.~moderate increasing, biased or binary trees and for weights with
$\alpha(t)\sigma(t)$ decreasing either polynomially or exponentially. We
also give some probabilistic applications for Gaussian summation schemes
on trees.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 47B06, Secondary: 06A06,
05C05
Submitted from: lifts at mail.rcom.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.3867
or
http://arXiv.org/abs/1006.3867
From alspach at fourier.math.okstate.edu Wed Jul 14 12:34:33 2010
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id 976D1D0B3A; Wed, 14 Jul 2010 12:34:33 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Maxim V. Balashov and Dusan Repovs
Message-Id: <20100714173433.976D1D0B3A at fourier.math.okstate.edu>
Date: Wed, 14 Jul 2010 12:34:33 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Weakly convex sets and modulus
of nonconvexity" by Maxim V. Balashov and Dusan Repovs.
Abstract: We consider a definition of a weakly convex set which is a
generalization of the notion of a weakly convex set in the sense of Vial
and a proximally smooth set in the sense of Clarke, from the case of the
Hilbert space to a class of Banach spaces with the modulus of convexity
of the second order. Using the new definition of the weakly convex set
with the given modulus of nonconvexity we prove a new retraction theorem
and we obtain new results about continuity of the intersection of two
continuous set-valued mappings (one of which has nonconvex images) and new
affirmative solutions of the splitting problem for selections. We also
investigate relationship between the new definition and the definition
of a proximally smooth set and a smooth set.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 46A55, 52A01, 52A07, 54C60, 54C65
Citation: J. Math. Anal. Appl. 371:1 (2010), 113-127
Submitted from: dusan.repovs at guest.arnes.si
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1007.0162
or
http://arXiv.org/abs/1007.0162
From alspach at fourier.math.okstate.edu Tue Jul 20 16:19:39 2010
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id D34D1D0B46; Tue, 20 Jul 2010 16:19:39 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Asuman Guven Aksoy and Grzegorz Lewicki
Message-Id: <20100720211939.D34D1D0B46 at fourier.math.okstate.edu>
Date: Tue, 20 Jul 2010 16:19:39 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Best approximation in numerical
radius" by Asuman Guven Aksoy and Grzegorz Lewicki.
Abstract: Let $X$ be a reflexive Banach space. In this paper we give a
necessary and sufficient condition for an operator $T\in \mathcal{K}(X)$
to have the best approximation in numerical radius from the convex
subset $\mathcal{U} \subset \mathcal{K}(X),$ where $\mathcal{K}(X)$
denotes the set of all linear, compact operators from $X$ into $X.$ We
will also present an application to minimal extensions with respect to
the numerical radius. In particular some results on best approximation
in norm will be generalized to the case of the numerical radius.
Archive classification: math.FA
Remarks: 13 pages
Submitted from: aaksoy at cmc.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1007.2205
or
http://arXiv.org/abs/1007.2205
From alspach at fourier.math.okstate.edu Tue Jul 20 16:21:12 2010
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id 372FCD0B46; Tue, 20 Jul 2010 16:21:12 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Asuman Guven Aksoy and Grzegorz Lewicki
Message-Id: <20100720212112.372FCD0B46 at fourier.math.okstate.edu>
Date: Tue, 20 Jul 2010 16:21:12 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Minimal projections with respect
to various norms" by Asuman Guven Aksoy and Grzegorz Lewicki.
Abstract: We will show that a theorem of Rudin \cite{wr1}, \cite{wr},
permits us to determine minimal projections not only with respect to
the operator norm but with respect to quasi-norms in operators ideals
and numerical radius in many concrete cases.
Archive classification: math.FA
Remarks: 16 pages
Submitted from: aaksoy at cmc.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1007.2214
or
http://arXiv.org/abs/1007.2214
From alspach at fourier.math.okstate.edu Tue Jul 20 16:22:41 2010
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id 90A4DD0B46; Tue, 20 Jul 2010 16:22:41 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Simon Luecking
Message-Id: <20100720212241.90A4DD0B46 at fourier.math.okstate.edu>
Date: Tue, 20 Jul 2010 16:22:41 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Subspaces of almost Daugavet
spaces" by Simon Luecking.
Abstract: We study the almost Daugavet property, a generalization of
the Daugavet property. It is analysed what kind of subspaces and sums
of Banach spaces with the almost Daugavet property have this property
as well. The main result of the paper is: if $Z$ is a closed subspace
of a separable almost Daugavet space $X$ such that the quotient space
$X/Z$ contains no copy of $\ell_1$, then $Z$ has the almost Daugavet
property, too.
Archive classification: math.FA
Mathematics Subject Classification: 46B04
Remarks: 5 pages
Submitted from: simon.luecking at fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1007.2916
or
http://arXiv.org/abs/1007.2916
From alspach at fourier.math.okstate.edu Tue Jul 20 16:24:34 2010
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id 0D0C9D0B46; Tue, 20 Jul 2010 16:24:33 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Qi Lu, Jiongmin Yong and Xu Zhang
Message-Id: <20100720212434.0D0C9D0B46 at fourier.math.okstate.edu>
Date: Tue, 20 Jul 2010 16:24:33 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Representation of Ito integrals
by Lebesgue/Bochner integrals" by Qi Lu, Jiongmin Yong and Xu Zhang.
Abstract: In [22], it was proved that as long as the integrand has
certain properties, the corresponding It\^o integral can be written as
a (parameterized) Lebesgue integral (or a Bochner integral). In this
paper, we show that such a question can be answered in a more positive
and refined way. To do this, we need to characterize the dual of the
Banach space of some vector-valued stochastic processes having different
integrability with respect to the time variable and the probability
measure. The later can be regarded as a variant of the classical Riesz
Representation Theorem, and therefore it will be useful in studying
other problems. Some remarkable consequences are presented as well,
including a reasonable definition of exact controllability for stochastic
differential equations and a condition which implies a Black-Scholes
market to be complete.
Archive classification: math.PR math.FA math.OC
Remarks: 26pages
Submitted from: xuzhang at amss.ac.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1007.2969
or
http://arXiv.org/abs/1007.2969
From alspach at fourier.math.okstate.edu Thu Aug 19 12:54:40 2010
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id 472DCD0CA8; Thu, 19 Aug 2010 12:54:40 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Y. Gordon, M. Junge, M. Meyer and S. Reisner
Message-Id: <20100819175440.472DCD0CA8 at fourier.math.okstate.edu>
Date: Thu, 19 Aug 2010 12:54:40 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The GL-l.u.st. constant and
asymmetry of the Kalton-Peck twisted sum in finite dimensions" by
Y. Gordon, M. Junge, M. Meyer and S. Reisner.
Abstract: We prove that the Kalton-Peck twisted sum $Z_2^n$ of
$n$-dimensional Hilbert spaces has GL-l.u.st.\ constant of order $\log
n$ and bounded GL constant. This is the first concrete example which
shows different explicit orders of growth in the GL and GL-l.u.st.\
constants. We discuss also the asymmetry constants of $Z_2^n$.
Archive classification: math.FA
Remarks: Proc. AMS, accepted
Submitted from: reisner at math.haifa.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1007.4692
or
http://arXiv.org/abs/1007.4692
From banach-bounces at math.okstate.edu Wed Sep 1 08:33:22 2010
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Date: Wed, 1 Sep 2010 06:24:45 -0500 (CDT)
From: elias <elias at math.missouri.edu>
To: banach at math.okstate.edu
Message-ID: <20100901062339.R75863 at home.math.missouri.edu>
MIME-Version: 1.0
X-Virus-Scanned: ClamAV using ClamSMTP
X-Mailman-Approved-At: Wed, 01 Sep 2010 08:31:56 -0500
Subject: [Banach] Nigel Kalton Has Died
Hi All,
My son called and said that Nigel's daughter told him that Nigel died.
Nigel suffered a severe stroke a couple of days ago and did not recover.
It is a devastating loss for all of us.
Elias
Elias Saab, Emeritus Professor
Department of Mathematics
202 Math Science Building
University of Missouri-Columbia
Columbia, MO 65211
Phone (Office) 573-884-0621
e-mail elias at math.missouri.edu
http://saab.org
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From banach-bounces at math.okstate.edu Thu Sep 2 07:54:05 2010
Return-Path: <banach-bounces at math.okstate.edu>
Date: Thu, 2 Sep 2010 01:23:37 -0500
Message-ID: <AANLkTin7T_nX18DK+VrN1rJBqRKfKY+GCpR3b_sY3+O6 at mail.gmail.com>
From: Elias Saab <eliassaab123 at gmail.com>
To: banach at math.okstate.edu
---------- Forwarded message ----------
From: Himmelberg, Glen R. <HimmelbergG at missouri.edu>
Date: Wed, Sep 1, 2010 at 2:22 PM
Subject: Memorial Service for Nigel Kalton
To: MU A&S Math all <MUA&SMathall at missouri.edu <MUA%26SMathall at missouri.edu>
>
Dear All:
The family of Nigel Kalton has scheduled a memorial service for Nigel on
Friday, October 1, from 1:00 to 3:00 pm at Reynolds Alumni Center. There
will be a service followed by a reception.
Sincerely,
Glen
-- Glen R. Himmelberg
Chair, Department of Mathematics
University of Missouri
Columbia, MO 65211
Phone: 573-882-6222
Fax: 573-882-1869
--
Elias Saab, Emeritus Professor
Department of Mathematics
202 Math Science Building
University of Missouri-Columbia
Columbia, MO 65211
Phone (Office 308 MSB) 573-882-4530
e-mail eliassaab123 at gmail.com
http://saab.org
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From banach-bounces at math.okstate.edu Tue Sep 7 16:58:36 2010
Return-Path: <banach-bounces at math.okstate.edu>
From: "Casazza, Peter" <casazzap at missouri.edu>
To: "banach at cauchy.math.okstate.edu" <banach at math.okstate.edu>
Date: Tue, 7 Sep 2010 15:27:21 -0500
Nigel J. Kalton of the University of Missouri passed
away from a stroke on August 31, 2010. There will
be a memorial service held at the Reynolds Alumni Center
on the MU campus from 1-3 pm on Friday, October 1.
The family has requested that in lieu of flowers,
donations be made to the Nigel Kalton Memorial
Scholarship. If you wish to contribute, please send a
check to the address below made out to
The University of Missouri with a notation that it is for the
Nigel Kalton Scholarship.
Nigel was a giant of a person and a mathematician.
He will be sadly missed.
Kimberly Dostoglou
Department of Mathematics
University of Missouri
Columbia, MO 65211
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Wed Sep 8 17:05:37 2010
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id A329CD0D79; Wed, 8 Sep 2010 17:05:37 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Tanja Eisner and Tamas Matrai
Message-Id: <20100908220537.A329CD0D79 at fourier.math.okstate.edu>
Date: Wed, 8 Sep 2010 17:05:37 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On typical properties of Hilbert
space operators" by Tanja Eisner and Tamas Matrai.
Abstract: We study the typical behavior of bounded linear operators
on infinite dimensional complex separable Hilbert spaces in the
norm, strong-star, strong, weak polynomial and weak topologies. In
particular, we investigate typical spectral properties, the problem of
unitary equivalence of typical operators, and their embeddability into
C_0-semigroups. Our results provide information on the applicability of
Baire category methods in the theory of Hilbert space operators.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 47A05, 47A10 (Primary) 54E52
(Secondary)
Remarks: 22 pages, submitted
Submitted from: talo at fa.uni-tuebingen.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1008.3326
or
http://arXiv.org/abs/1008.3326
From alspach at fourier.math.okstate.edu Wed Sep 8 17:07:02 2010
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id 92CEED0D79; Wed, 8 Sep 2010 17:07:02 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Luis Rademacher
Message-Id: <20100908220702.92CEED0D79 at fourier.math.okstate.edu>
Date: Wed, 8 Sep 2010 17:07:02 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On the monotonicity of the expected
volume of a random simplex" by Luis Rademacher.
Abstract: Let a random simplex in a d-dimensional convex body be the
convex hull of d+1 random points from the body. We study the following
question: As a function of the convex body, is the expected volume of
a random simplex monotone non-decreasing under inclusion? We show that
this holds if d is 1 or 2, and does not hold if d >= 4. We also prove
similar results for higher moments of the volume of a random simplex, in
particular for the second moment, which corresponds to the determinant of
the covariance matrix of the convex body. These questions are motivated
by the slicing conjecture.
Archive classification: math.PR math.FA math.MG
Submitted from: lrademac at cse.ohio-state.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1008.3944
or
http://arXiv.org/abs/1008.3944
From alspach at fourier.math.okstate.edu Wed Sep 8 17:08:24 2010
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To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Nikos Yannakakis
Message-Id: <20100908220824.D6CFED0D79 at fourier.math.okstate.edu>
Date: Wed, 8 Sep 2010 17:08:24 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Stampacchia's property,
self-duality and orthogonality relations" by Nikos Yannakakis.
Abstract: We show that if the conclusion of the well known Stampacchia
Theorem, on variational inequalities, holds on a Banach space X, then X
is isomorphic to a Hilbert space. Motivated by this we obtain a relevant
result concerning self-dual Banach spaces and investigate some connections
between existing notions of orthogonality and self-duality. Moreover, we
revisit the notion of the cosine of a linear operator and show that it can
be used to characterize Hilbert space structure. Finally, we present some
consequences of our results to quadratic forms and to evolution triples.
Archive classification: math.FA
Submitted from: nyian at math.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1008.4958
or
http://arXiv.org/abs/1008.4958
From alspach at fourier.math.okstate.edu Wed Sep 8 17:09:45 2010
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id C795FD0D79; Wed, 8 Sep 2010 17:09:45 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Iosif Pinelis
Message-Id: <20100908220945.C795FD0D79 at fourier.math.okstate.edu>
Date: Wed, 8 Sep 2010 17:09:45 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On the von Bahr--Esseen inequality"
by Iosif Pinelis.
Abstract: The well-known von Bahr--Esseen bound on the absolute pth
moments of martingales with p in (1,2] is extended to a large class of
moment functions, and now with a best possible constant factor (which
depends on the moment function). As an application, measure concentration
inequalities for separately Lipschitz functions on product spaces are
obtained. Relations with p-uniformly smooth and q-uniformly convex normed
spaces are discussed.
Archive classification: math.PR math.FA
Mathematics Subject Classification: Primary 60E15, 60B11, 62G10, secondary
46B09, 46B20, 46B10
Submitted from: ipinelis at mtu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1008.5350
or
http://arXiv.org/abs/1008.5350
From alspach at fourier.math.okstate.edu Wed Sep 8 17:10:48 2010
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id CBAC7D0D79; Wed, 8 Sep 2010 17:10:48 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Mohammad Sal Moslehian and John M. Rassias
Message-Id: <20100908221048.CBAC7D0D79 at fourier.math.okstate.edu>
Date: Wed, 8 Sep 2010 17:10:48 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A characterization of inner
product spaces" by Mohammad Sal Moslehian and John M. Rassias.
Abstract: In this paper we present a new criterion on
characterization of real inner product spaces. We conclude
that a real normed space $(X, \|\cdot\|)$ is an inner product
space if $$\sum_{\varepsilon_i \in \{-1,1\}} \left\|x_1 +
\sum_{i=2}^k\varepsilon_ix_i\right\|^2=\sum_{\varepsilon_i \in \{-1,1\}}
\left(\|x_1\| + \sum_{i=2}^k\varepsilon_i\|x_i\|\right)^2\,,$$ for some
positive integer $k\geq 2$ and all $x_1, \ldots, x_k \in X$. Conversely,
if $(X, \|\cdot\|)$ is an inner product space, then the equality above
holds for all $k\geq 2$ and all $x_1, \ldots, x_k \in X$.
Archive classification: math.FA math.CA
Mathematics Subject Classification: Primary 46C15, Secondary 46B20, 46C05
Remarks: 8 Pages, to appear in Kochi J. Math. (Japan)
Submitted from: moslehian at ferdowsi.um.ac.ir
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.0079
or
http://arXiv.org/abs/1009.0079
From banach-bounces at math.okstate.edu Wed Sep 1 08:33:22 2010
Date: Wed, 1 Sep 2010 06:24:45 -0500 (CDT)
From: elias <elias at math.missouri.edu>
To: banach at math.okstate.edu
Subject: [Banach] Nigel Kalton Has Died
Reply-To: Elias Saab <elias at math.missouri.edu>
Hi All,
My son called and said that Nigel's daughter told him that Nigel died.
Nigel suffered a severe stroke a couple of days ago and did not recover.
It is a devastating loss for all of us.
Elias
Elias Saab, Emeritus Professor
Department of Mathematics
202 Math Science Building
University of Missouri-Columbia
Columbia, MO 65211
Phone (Office) 573-884-0621
e-mail elias at math.missouri.edu
http://saab.org
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From banach-bounces at math.okstate.edu Thu Sep 2 07:54:05 2010
Date: Thu, 2 Sep 2010 01:23:37 -0500
From: Elias Saab <eliassaab123 at gmail.com>
To: banach at math.okstate.edu
Subject: [Banach] Memorial Service for Nigel Kalton
---------- Forwarded message ----------
From: Himmelberg, Glen R. <HimmelbergG at missouri.edu>
Date: Wed, Sep 1, 2010 at 2:22 PM
Subject: Memorial Service for Nigel Kalton
To: MU A&S Math all <MUA&SMathall at missouri.edu <MUA%26SMathall at missouri.edu>
>
Dear All:
The family of Nigel Kalton has scheduled a memorial service for Nigel on
Friday, October 1, from 1:00 to 3:00 pm at Reynolds Alumni Center. There
will be a service followed by a reception.
Sincerely,
Glen
-- Glen R. Himmelberg
Chair, Department of Mathematics
University of Missouri
Columbia, MO 65211
Phone: 573-882-6222
Fax: 573-882-1869
--
Elias Saab, Emeritus Professor
Department of Mathematics
202 Math Science Building
University of Missouri-Columbia
Columbia, MO 65211
Phone (Office 308 MSB) 573-882-4530
e-mail eliassaab123 at gmail.com
http://saab.org
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From banach-bounces at math.okstate.edu Tue Sep 7 16:58:36 2010
Subject: [Banach] Please Post This
From: "Casazza, Peter" <casazzap at missouri.edu>
To: "banach at cauchy.math.okstate.edu" <banach at math.okstate.edu>
Date: Tue, 7 Sep 2010 15:27:21 -0500
Nigel J. Kalton of the University of Missouri passed
away from a stroke on August 31, 2010. There will
be a memorial service held at the Reynolds Alumni Center
on the MU campus from 1-3 pm on Friday, October 1.
The family has requested that in lieu of flowers,
donations be made to the Nigel Kalton Memorial
Scholarship. If you wish to contribute, please send a
check to the address below made out to
The University of Missouri with a notation that it is for the
Nigel Kalton Scholarship.
Nigel was a giant of a person and a mathematician.
He will be sadly missed.
Kimberly Dostoglou
Department of Mathematics
University of Missouri
Columbia, MO 65211
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From banach-bounces at math.okstate.edu Fri Sep 17 11:56:17 2010
Date: Fri, 17 Sep 2010 18:17:45 +0200
From: IntMedVec Murcia 2011 <banach at um.es>
To: banach at math.okstate.edu
Subject: [Banach] Meeting: Integration,
Vector Measures and Related Topics IV'' Dedicated to Joe Diestel.
Murcia 2011
Meeting: Integration, Vector Measures and Related Topics IV''
Dedicated to Joe Diestel.
University of Murcia, Murcia, Spain March 2 - March 5, 2011
Description: The aim of this four day conference is to bring together
experienced and novice researchers interested in Integration, Vector
Measures and their Applications. The conference will feature a series
of plenary and short lectures as well as a mini-course and contributed
posters on recent advances in the subject. The previous meetings of
this series of conferences were held in Valencia in 2004, Sevilla in
2006 and Eichst=E4tt in 2008. Partial support for a small number of
participants is expected to be available. Recent recipients of
doctoral degrees and pre-doc students are encouraged to apply. The
meeting will take place in La Manga del Mar Menor, Murcia, from March
2? March 5, 2011 (both days included). It will be organized by the
Functional Analysis Group of the University of Murcia.
Information: http://www.um.es/beca/Murcia2011/index.php
Sponsors: UMU, MCIN, iMath Consolider, Fundacion Seneca CARM
On behalf of the organizers.
Integration, Vector Measures and Related Topics IV.
Murcia. March 2-5. 2011
http://www.um.es/beca/Murcia2011/index.php
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Thu Sep 30 13:50:25 2010
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id B1F65D0DC5; Thu, 30 Sep 2010 13:50:25 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by V.L. Dolnikov and R.N. Karasev
Message-Id: <20100930185025.B1F65D0DC5 at fourier.math.okstate.edu>
Date: Thu, 30 Sep 2010 13:50:25 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Dvoretzky type theorems for
multivariate polynomials and sections of convex bodies" by V.L. Dolnikov
and R.N. Karasev.
Abstract: In this paper we prove the Gromov--Milman conjecture (the
Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$,
and improve bounds on the number $n(d,k)$ in the analogous conjecture
for odd degrees $d$ (this case is known as the Birch theorem) and
complex polynomials.
We also consider a stronger conjecture on the homogeneous polynomial fields
in the canonical bundle over real and complex Grassmannians. The latter
conjecture is much stronger and false in general, but it is proved in
the cases of $d=2$ (for $k$'s of certain type), odd $d$, the complex
Grassmannian (for odd and even $d$ and any $k$). Corollaries for the
John ellipsoid of projections or sections of a convex body are deduced
from the case $d=2$ of the polynomial field conjecture.
Archive classification: math.MG math.AT math.CO math.FA
Mathematics Subject Classification: 46B20, 05D10, 26C10, 52A21, 52A23,
55M35
Submitted from: r_n_karasev at mail.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.0392
or
http://arXiv.org/abs/1009.0392
From alspach at fourier.math.okstate.edu Thu Sep 30 13:51:54 2010
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id 8C875D0DC5; Thu, 30 Sep 2010 13:51:54 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Gideon Schechtman
Message-Id: <20100930185154.8C875D0DC5 at fourier.math.okstate.edu>
Date: Thu, 30 Sep 2010 13:51:54 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Tight embedding of subspaces of
$L_p$ in $\ell_p^n$ for even $p$" by Gideon Schechtman.
Abstract: Using a recent result of Batson, Spielman and Srivastava,
We obtain a tight estimate on the dimension of $\ell_p^n$, $p$ an even
integer, needed to almost isometrically contain all $k$-dimensional
subspaces of $L_p$.
Archive classification: math.FA
Submitted from: gideon at weizmann.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.1061
or
http://arXiv.org/abs/1009.1061
From alspach at fourier.math.okstate.edu Thu Sep 30 13:53:21 2010
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id 9256BD0DC5; Thu, 30 Sep 2010 13:53:21 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Daniel Carando, Veronica Dimant, and Santiago Muro
Message-Id: <20100930185321.9256BD0DC5 at fourier.math.okstate.edu>
Date: Thu, 30 Sep 2010 13:53:21 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Every Banach ideal of polynomials
is compatible with an operator ideal" by Daniel Carando, Veronica Dimant,
and Santiago Muro.
Abstract: We show that for each Banach ideal of homogeneous polynomials,
there exists a (necessarily unique) Banach operator ideal compatible with
it. Analogously, we prove that any ideal of $n$-homogeneous polynomials
belongs to a coherent sequence of ideals of $k$-homogeneous polynomials.
Archive classification: math.FA
Mathematics Subject Classification: 47H60, 47L20, 47L22 (Primary) 46G25
(Secondary)
Remarks: 12 pages
Submitted from: smuro at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.1064
or
http://arXiv.org/abs/1009.1064
From alspach at fourier.math.okstate.edu Thu Sep 30 13:54:52 2010
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id 65711D0DC5; Thu, 30 Sep 2010 13:54:52 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Jan Vybiral
Message-Id: <20100930185452.65711D0DC5 at fourier.math.okstate.edu>
Date: Thu, 30 Sep 2010 13:54:52 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Average best $m$-term
approximation" by Jan Vybiral.
Abstract: We introduce the concept of average best $m$-term
approximation widths with respect to a probability measure on the unit
ball of $\ell_p^n$. We estimate these quantities for the embedding
$id:\ell_p^n\to\ell_q^n$ with $0<p\le q\le \infty$ for the normalized
cone and surface measure. Furthermore, we consider certain tensor product
weights and show that a typical vector with respect to such a measure
exhibits a strong compressible (i.e. nearly sparse) structure.
Archive classification: math.FA math.NA math.ST stat.TH
Mathematics Subject Classification: 41A46 (Primary) 46B20, 60B11
(Secondary)
Remarks: 2 figures
Submitted from: jan.vybiral at oeaw.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.1751
or
http://arXiv.org/abs/1009.1751
From alspach at fourier.math.okstate.edu Thu Sep 30 13:56:19 2010
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X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 889D5D0DC5; Thu, 30 Sep 2010 13:56:19 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Thierry Gallay and Denis Serre
Message-Id: <20100930185619.889D5D0DC5 at fourier.math.okstate.edu>
Date: Thu, 30 Sep 2010 13:56:19 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The numerical measure of a complex
matrix" by Thierry Gallay and Denis Serre.
Abstract: We introduce and carefully study a natural probability measure
over the numerical range of a complex matrix $A \in M_n(\C)$. This
numerical measure $\mu_A$ can be defined as the law of the random
variable $<AX,X> \in \C$ when the vector $X \in \C^n$ is uniformly
distributed on the unit sphere. If the matrix $A$ is normal, we show
that $\mu_A$ has a piecewise polynomial density $f_A$, which can be
identified with a multivariate $B$-spline. In the general (nonnormal)
case, we relate the Radon transform of $\mu_A$ to the spectrum of a
family of Hermitian matrices, and we deduce an explicit representation
formula for the numerical density which is appropriate for theoretical
and computational purposes. As an application, we show that the density
$f_A$ is polynomial in some regions of the complex plane which can be
characterized geometrically, and we recover some known results about
lacunas of symmetric hyperbolic systems in $2+1$ dimensions. Finally,
we prove under general assumptions that the numerical measure of a
matrix $A \in M_n(\C)$ concentrates to a Dirac mass as the size $n$
goes to infinity.
Archive classification: math.FA math.PR math.SP
Mathematics Subject Classification: 47A12, 28A33, 44A12, 65D07, 35L40,
60F05
Remarks: 41 pages, 5 figures
Submitted from: thierry.gallay at ujf-grenoble.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.1522
or
http://arXiv.org/abs/1009.1522
From alspach at fourier.math.okstate.edu Thu Sep 30 13:57:25 2010
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 75BC5D0DC5; Thu, 30 Sep 2010 13:57:25 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Elias Pipping
Message-Id: <20100930185725.75BC5D0DC5 at fourier.math.okstate.edu>
Date: Thu, 30 Sep 2010 13:57:25 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "L- and M-structure in lush spaces"
by Elias Pipping.
Abstract: Let $X$ be a Banach space which is lush. It is shown that if a
subspace of $X$ is either an L-summand or an M-ideal then it is also lush.
Archive classification: math.FA
Submitted from: pipping at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.2232
or
http://arXiv.org/abs/1009.2232
From alspach at fourier.math.okstate.edu Thu Sep 30 13:58:35 2010
Return-Path: <alspach at fourier.math.okstate.edu>
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id 23457D0DC5; Thu, 30 Sep 2010 13:58:35 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Stanislav Shkarin
Message-Id: <20100930185835.23457D0DC5 at fourier.math.okstate.edu>
Date: Thu, 30 Sep 2010 13:58:35 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A complete locally convex space of
countable dimension admitting an operator with no invariant subspaces"
by Stanislav Shkarin.
Abstract: We construct a complete locally convex topological vector space
$X$ of countable algebraic dimension and a continuous linear operator
$T:X\to X$ such that $T$ has no non-trivial closed invariant subspaces.
Archive classification: math.FA
Mathematics Subject Classification: 47A16
Submitted from: s.shkarin at qub.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.2644
or
http://arXiv.org/abs/1009.2644
From alspach at fourier.math.okstate.edu Thu Sep 30 13:59:47 2010
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id 57291D0DC5; Thu, 30 Sep 2010 13:59:47 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Daniel Pellegrino
Message-Id: <20100930185947.57291D0DC5 at fourier.math.okstate.edu>
Date: Thu, 30 Sep 2010 13:59:47 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A note on the best constants for
the Bohnenblust-Hille inequality" by Daniel Pellegrino.
Abstract: In this note we show that a recent new proof of
Bohnenblust-Hille inequality, due to Defant et al, combined with the
better known constant for Littlewood 4/3 theorem and the optimal
constants of Khinchin inequality, due to Haagerup, provide quite
better estimates for the constants involved in the Bohnenblust-Hille
inequality. For example, if $2\leq m\leq13,$ we show that the constants
$C_{m}=2^{(m-1)/2}$ can be replaced by $2^{\frac{m^{2}+m-6}{4m}%
}K_{G}^{2/m}$, which are substantially better than $C_{m}$ (here $K_{G}$
denotes the complex Grothendieck
Archive classification: math.FA
Remarks: 7 pages
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.2717
or
http://arXiv.org/abs/1009.2717
From alspach at fourier.math.okstate.edu Thu Sep 30 14:01:32 2010
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id DCABFD0DC5; Thu, 30 Sep 2010 14:01:32 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Niels Jakob Laustsen, Edward Odell, Thomas Schlumprecht, and Andras Zsak
Message-Id: <20100930190132.DCABFD0DC5 at fourier.math.okstate.edu>
Date: Thu, 30 Sep 2010 14:01:32 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Dichotomy theorems for
random matrices and closed ideals of operators on $\big(\bigoplus
_{n=1}^\infty\ell_1^n \big)_{\mathrm{c}_0}$" by Niels Jakob Laustsen,
Edward Odell, Thomas Schlumprecht, and Andras Zsak.
Abstract: We prove two dichotomy theorems about sequences of operators
into $L_1$ given by random matrices. In the second theorem we assume
that the entries of each random matrix form a sequence of independent,
symmetric random variables. Then the corresponding sequence of operators
either uniformly factor the identity operators on $\ell_1^k$ $(k\in\mathbb
N$) or uniformly approximately factor through $\mathrm{c}_0$. The
first theorem has a slightly weaker conclusion still related to
factorization properties but makes no assumption on the random
matrices. Indeed, it applies to operators defined on an arbitrary
sequence of Banach spaces. These results provide information on the
closed ideal structure of the Banach algebra of all operators on the
space $\big(\bigoplus_{n=1}^\infty\ell_1^n \big)_{\mathrm{c}_0}$.
Archive classification: math.FA
Mathematics Subject Classification: 47L10 (primary), 46B09, 46B42, 47L20,
46B45 (secondary)
Remarks: 22 pages
Submitted from: andras.zsak at maths.nottingham.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.2923
or
http://arXiv.org/abs/1009.2923
From alspach at fourier.math.okstate.edu Thu Sep 30 14:02:35 2010
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id 7794DD0DC5; Thu, 30 Sep 2010 14:02:35 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Sonia Berrios and Geraldo Botelho
Message-Id: <20100930190235.7794DD0DC5 at fourier.math.okstate.edu>
Date: Thu, 30 Sep 2010 14:02:35 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Approximation properties determined
by operator ideals" by Sonia Berrios and Geraldo Botelho.
Abstract: Given an operator ideal I, a Banach space E has the
I-approximation property if operators on E can be uniformly approximated
on compact subsets of E by operators belonging to I. In this paper the I-
approximation property is studied in projective tensor products, spaces
of linear functionals, spaces of homogeneous polynomials (in particular,
spaces of linear operators), spaces of holomorphic functions and their
preduals.
Archive classification: math.FA
Remarks: 24 pages
Submitted from: botelho at ufu.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.2977
or
http://arXiv.org/abs/1009.2977
From gesztesyf at missouri.edu Sun Oct 17 16:02:49 2010
From: Fritz Gesztesy <gesztesyf at missouri.edu>
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: quoted-printable
Subject: N. Kalton
Date: Sun, 17 Oct 2010 15:46:23 -0500
Message-Id: <3BFA8077-B14D-4807-8A1C-AB862A912EE8 at missouri.edu>
Cc: alspach at math.okstate.edu,
Fritz Gesztesy <gesztesyf at missouri.edu>
To: banach at math.okstate.edu
X-Virus-Scanned: ClamAV using ClamSMTP
Dear Colleagues,
The Department of Mathematics of the University of Missouri, Columbia,
MO, is in the process of establishing a website in honor of Nigel
Kalton, who passed away recently.
The website will consist of several parts. We hope to be able to post
downloadable pdf files of his works, supply a list of his students and
co-authors, indicate his editorial activity, establish a photo gallery,
and comment on some of his other significant activities, such as playing
chess. We also plan to have a section in which students, collaborators,
and friends will be able to recall fond reminiscences and express their
appreciation of Nigel.
Apart from alerting you to this activity, the purpose of this message is
to solicit contributions you may be able to make to this Kalton Memorial
Website, such as, photos, stories, reminiscences, etc.
Please send all material to
Fritz Gesztesy
Department of Mathematics
University of Missouri
Columbia, MO 65211
USA
E-mail: gesztesyf at missouri.edu
Thanks, and best regards,
Fritz Gesztesy
PLEASE NOTE THE CHANGE OF E-MAIL ADDRESS: gesztesyf at missouri.edu
Department of Mathematics, University of Missouri, Columbia, MO 65211,
USA
Office: (573) 882 4386
FAX: (573) 882 1869
Department: (573) 882 6221
Home: (573) 443 8913
E-mail: gesztesyf at missouri.edu
http://www.math.missouri.edu/personnel/faculty/gesztesyf.html
From alspach at fourier.math.okstate.edu Mon Oct 18 16:12:55 2010
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id B1E14D0E25; Mon, 18 Oct 2010 16:12:55 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Amir Nasseri
Message-Id: <20101018211255.B1E14D0E25 at fourier.math.okstate.edu>
Date: Mon, 18 Oct 2010 16:12:55 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On the existence of J-class
operators" by Amir Nasseri.
Abstract: In this note we answer in the negative the question raised by
G.Costakis and A.Manoussos, whether there exists a J-class operator on
every non-separable Banach space. In par- ticular we show that there
exists a non-separable Banach space constructed by A.Arvanitakis,
S.Argyros and A.Tolias such that the J-set of every operator on this
space has empty interior for each non-zero vector. On the other hand,
on non-separable spaces which are reflexive there always exist a J-class
operator.
Archive classification: math.FA
Remarks: 8 pages, hypercyclicity, J-class operators
Submitted from: amir.nasseri at uni-dortmund.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.3461
or
http://arXiv.org/abs/1009.3461
From alspach at fourier.math.okstate.edu Mon Oct 18 16:14:27 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 2E4DDD0E25; Mon, 18 Oct 2010 16:14:27 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Shlomo Reisner, Carsten Schutt and Elisabeth M. Werner
Message-Id: <20101018211427.2E4DDD0E25 at fourier.math.okstate.edu>
Date: Mon, 18 Oct 2010 16:14:27 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A note on Mahler's conjecture"
by Shlomo Reisner, Carsten Schutt and Elisabeth M. Werner.
Abstract: Let $K$ be a convex body in $\mathbb{R}^n$ with Santal\'o
point at $0$. We show that if $K$ has a point on the boundary with
positive generalized Gau{\ss} curvature, then the volume product $|K|
|K^\circ|$ is not minimal. This means that a body with minimal volume
product has Gau{\ss} curvature equal to $0$ almost everywhere and thus
suggests strongly that a minimal body is a polytope.
Archive classification: math.FA
Mathematics Subject Classification: 52A20
Submitted from: elisabeth.werner at case.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.3583
or
http://arXiv.org/abs/1009.3583
From alspach at fourier.math.okstate.edu Mon Oct 18 16:15:36 2010
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id 93642D0E25; Mon, 18 Oct 2010 16:15:36 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Timur Oikhberg and Christian Rosendal
Message-Id: <20101018211536.93642D0E25 at fourier.math.okstate.edu>
Date: Mon, 18 Oct 2010 16:15:36 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Subspace structure of some operator
and Banach spaces" by Timur Oikhberg and Christian Rosendal.
Abstract: We construct a family of separable Hilbertian operator spaces,
such that the relation of complete isomorphism between the subspaces of
each member of this family is complete $\ks$. We also investigate some
interesting properties of completely unconditional bases of the spaces
from this family. In the Banach space setting, we construct a space for
which the relation of isometry of subspaces is equivalent to equality
of real numbers.
Archive classification: math.FA math.LO
Remarks: 30 pages
Submitted from: toikhber at math.uci.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.3591
or
http://arXiv.org/abs/1009.3591
From alspach at fourier.math.okstate.edu Mon Oct 18 16:17:10 2010
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id 0288FD0E25; Mon, 18 Oct 2010 16:17:09 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Paul F. X. Mueller
Message-Id: <20101018211710.0288FD0E25 at fourier.math.okstate.edu>
Date: Mon, 18 Oct 2010 16:17:09 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A thin-thick decomposition for
Hardy martingales" by Paul F. X. Mueller.
Abstract: We prove thin-thick decompositions, for the class
of Hardy martingales and thereby strengthen its square function
characterization. We apply the underlying method to several classical
martingale inequalities, for which we give new proofs .
Archive classification: math.FA
Submitted from: pfxm at bayou.uni-linz.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.3629
or
http://arXiv.org/abs/1009.3629
From alspach at fourier.math.okstate.edu Mon Oct 18 16:19:20 2010
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X-Original-To: alspach
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id 42F69D0E25; Mon, 18 Oct 2010 16:19:20 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Timur Oikhberg
Message-Id: <20101018211920.42F69D0E25 at fourier.math.okstate.edu>
Date: Mon, 18 Oct 2010 16:19:20 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Rate of decay of s-numbers"
by Timur Oikhberg.
Abstract: For an operator $T \in B(X,Y)$, we denote by $a_m(T)$,
$c_m(T)$, $d_m(T)$, and $t_m(T)$ its approximation, Gelfand, Kolmogorov,
and absolute numbers. We show that, for any infinite dimensional Banach
spaces $X$ and $Y$, and any sequence $\alpha_m \searrow 0$, there exists
$T \in B(X,Y)$ for which the inequality $$ 3 \alpha_{\lceil m/6 \rceil}
\geq a_m(T) \geq \max\{c_m(t), d_m(T)\} \geq \min\{c_m(t), d_m(T)\}
\geq t_m(T) \geq \alpha_m/9 $$ holds for every $m \in \N$. Similar
results are obtained for other $s$-scales.
Archive classification: math.FA math.NA
Mathematics Subject Classification: 46A3, 46B28, 47B10
Submitted from: toikhber at math.uci.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.4278
or
http://arXiv.org/abs/1009.4278
From alspach at fourier.math.okstate.edu Mon Oct 18 16:24:48 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 64868D0E25; Mon, 18 Oct 2010 16:24:48 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Ramon van Handel
Message-Id: <20101018212448.64868D0E25 at fourier.math.okstate.edu>
Date: Mon, 18 Oct 2010 16:24:48 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "The universal Glivenko-Cantelli
property" by Ramon van Handel.
Abstract: Let F be a separable uniformly bounded family of measurable
functions on a standard measurable space, and let N_{[]}(F,\epsilon,\mu)
be the smallest number of \epsilon-brackets in L^1(\mu) needed to cover
F. The following are equivalent:
1. F is a universal Glivenko-Cantelli class.
2. N_{[]}(F,\epsilon,\mu)<\infty for every \epsilon>0 and every
probability
measure \mu.
3. F is totally bounded in L^1(\mu) for every probability measure
\mu. 4. F does not contain a Boolean \sigma-independent sequence.
In particular, universal Glivenko-Cantelli classes are uniformity
classes for
general sequences of almost surely convergent random measures.
Archive classification: math.PR math.FA math.MG math.ST stat.TH
Mathematics Subject Classification: 60F15, 60B10, 41A46
Remarks: 15 pages
Submitted from: rvan at princeton.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.4434
or
http://arXiv.org/abs/1009.4434
From alspach at fourier.math.okstate.edu Mon Oct 18 16:26:07 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 692D4D0E25; Mon, 18 Oct 2010 16:26:07 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Andrea Marchese and Clemente Zanco
Message-Id: <20101018212607.692D4D0E25 at fourier.math.okstate.edu>
Date: Mon, 18 Oct 2010 16:26:07 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "On a question by Corson about
point-finite coverings" by Andrea Marchese and Clemente Zanco.
Abstract: We answer in the affirmative the following question raised
by H. H. Corson in 1961: "Is it possible to cover every Banach space
X by bounded convex sets with nonempty interior in such a way that no
point of X belongs to infinitely many of them?" Actually we show the way
to produce in every Banach space X a bounded convex tiling of order 2,
i.e. a covering of X by bounded convex closed sets with nonempty interior
(tiles) such that the interiors are pairwise disjoint and no point of
X belongs to more than two tiles.
Archive classification: math.FA
Remarks: to appear on Israel J. Math
Submitted from: marchese at mail.dm.unipi.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.4681
or
http://arXiv.org/abs/1009.4681
From alspach at fourier.math.okstate.edu Mon Oct 18 16:27:07 2010
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X-Original-To: alspach
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 94816D0E25; Mon, 18 Oct 2010 16:27:07 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Daniel Pellegrino and Joedson Santos
Message-Id: <20101018212707.94816D0E25 at fourier.math.okstate.edu>
Date: Mon, 18 Oct 2010 16:27:07 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Abstract ideals of absolutely
summing multilinear operators" by Daniel Pellegrino and Joedson Santos.
Abstract: This paper has a twofold purpose: to present an overview of the
different multi-ideals that generalize the concept of absolutely summing
operators and to sketch the beginning of a research project related
to an objective search of \textquotedblleft perfect\textquotedblright\
multilinear extensions of the ideal of absolutely summing operators. The
final section contains some open problems that may indicate lines for
future investigation.
Archive classification: math.FA
Remarks: 10 pages
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1009.4807
or
http://arXiv.org/abs/1009.4807
From banach-bounces at math.okstate.edu Fri Oct 22 08:41:21 2010
Return-Path: <banach-bounces at math.okstate.edu>
Mime-Version: 1.0 (Apple Message framework v752.2)
Message-Id: <76D30372-308B-49B4-89A4-71B2C88421C5 at math.jussieu.fr>
To: banach at math.okstate.edu
From: Gilles Godefroy <godefroy at math.jussieu.fr>
Date: Fri, 22 Oct 2010 15:49:24 +0200
Subject: Papers of Nigel Kalton
Nigel Kalton passed away on 31 August, 2010. He had work in progress
and the information available so far leaves it unclear whether some
articles, which were found on his desk in apparently final form, have
been submitted or not. The titles are:
- Hermitian operators on complex Banach lattices and a problem of
Garth Dales.
- Uniform homeomorphisms of Banach spaces and asymptotic structure.
- Examples of uniformly homeomorphic Banach spaces.
- The uniform structure of Banach spaces.
We would be grateful for any information on the status of these
papers, which will be submitted in Nigel's name if needed. Please
kindly write to casazzap at missouri.edu and to godefroy at math.jussieu.fr
if you know something. Your help is appreciated.
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From banach-bounces at math.okstate.edu Sun Oct 24 14:32:30 2010
Date: Sun, 24 Oct 2010 12:13:50 -0500
Message-ID: <AANLkTik8agLr_DTTqbh_MtCShYhDf3cqENPxaoXQRBRo at mail.gmail.com>
From: Elias Saab <eliassaab123 at gmail.com>
To: banach at math.okstate.edu
---------- Forwarded message ----------
From: Debra Woods <dwoods2 at illinois.edu>
Date: Sun, Oct 24, 2010 at 9:21 AM
Subject: Fwd: J Jerry Uhl
To: "jerryfriends at cm.math.uiuc.edu" <jerryfriends at cm.math.uiuc.edu>
Hello all,
I wanted to let you all know that Jerry passed away last night in his sleep.
I'll send more information as I find it out.
Debra
Begin forwarded message:
*From: *"Mr. Jac M Knoop" <jac at amsincorporated.net>
*Date: *October 24, 2010 8:33:37 AM CDT
*To: *Debra Woods <dwoods at cm.math.uiuc.edu>, Deborah Hughes Hallett <
deborah_hughes_hallett at harvard.edu>, Suzanne Smith <suzannesmith at hughes.net>,
Bill Davis <nudge_1994 at yahoo.com>, Mr&Mrs Bill & Mary Davis <
bigdogmom1960 at yahoo.com>, Linda Krukewitt <krukfarms at yahoo.com>
*Subject: **J Jerry Uhl*
Dear Friends,
This morning our friend and neighbor, John Jerry Uhl, passed away in his
sleep.
Everything looked very peaceful.
No details of the funeral or cremation are available at this time, Jerry's
sister is
on her way to Illinois and we will have more information later.
*Sincerely,*
Jac M Knoop
AMS Incorporated
Manufacturers Representatives and Distributors
"The work will wait while you show a child the rainbow,
but the rainbow won't wait while you finish the work."
--
Elias Saab, Emeritus Professor
Department of Mathematics
202 Math Science Building
University of Missouri-Columbia
Columbia, MO 65211
Phone (Office 308 MSB) 573-882-4530
e-mail eliassaab123 at gmail.com
http://saab.org
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Fri Oct 29 17:38:01 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
Delivered-To: alspach at fourier.math.okstate.edu
Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 60815D0E20; Fri, 29 Oct 2010 17:38:01 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Vegard Lima and N. Lovasoa Randrianarivony
Message-Id: <20101029223801.60815D0E20 at fourier.math.okstate.edu>
Date: Fri, 29 Oct 2010 17:38:01 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Property $(\beta)$ and uniform
quotient maps" by Vegard Lima and N. Lovasoa Randrianarivony.
Abstract: In 1999, Bates, Johnson, Lindenstrauss, Preiss and Schechtman
asked whether a Banach space that is a uniform quotient of $\ell_p$,
$1 < p \neq 2 < \infty$, must be isomorphic to a linear quotient of
$\ell_p$. We apply the geometric property $(\beta)$ of Rolewicz to the
study of uniform and Lipschitz quotient maps, and answer the above
question positively for the case $1<p<2$. We also give a necessary
condition for a Banach space to have $c_0$ as a uniform quotient.
Archive classification: math.FA math.MG
Submitted from: nrandria at slu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1010.0184
or
http://arXiv.org/abs/1010.0184
From alspach at fourier.math.okstate.edu Fri Oct 29 17:39:54 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
Delivered-To: alspach at fourier.math.okstate.edu
Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 84BB9D0E20; Fri, 29 Oct 2010 17:39:54 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Volker Runde
Message-Id: <20101029223954.84BB9D0E20 at fourier.math.okstate.edu>
Date: Fri, 29 Oct 2010 17:39:54 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "A new and simple proof of
Schauder's theorem" by Volker Runde.
Abstract: Schauder's theorem asserts that a bounded linear operator
between Banach spaces is compact if ad only if its adjoint is. We give a
new proof of this result, which is both short and completely elementary
in the sense that it does not depend on anything beyond basic functional
analysis, i.e., the Hahn--Banach theorem and some of its consequences;
in particular, we avoid the Arzela--Ascoli theorem (and any kind of
related diagonal argument).
Archive classification: math.FA
Submitted from: vrunde at ualberta.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1010.1298
or
http://arXiv.org/abs/1010.1298
From alspach at fourier.math.okstate.edu Fri Oct 29 17:41:36 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
Delivered-To: alspach at fourier.math.okstate.edu
Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 1F95ED0E20; Fri, 29 Oct 2010 17:41:36 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Maxim V. Balashov and Dusan Repovs
Message-Id: <20101029224136.1F95ED0E20 at fourier.math.okstate.edu>
Date: Fri, 29 Oct 2010 17:41:36 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Polyhedral approximations of
strictly convex compacta" by Maxim V. Balashov and Dusan Repovs.
Abstract: We consider polyhedral approximations of strictly convex
compacta in finite dimensional Euclidean spaces (such compacta are also
uniformly convex). We obtain the best possible estimates for errors of
considered approximations in the Hausdorff metric. We also obtain new
estimates of an approximate algorithm for finding the convex hulls.
Archive classification: math.FA math.GN math.MG
Mathematics Subject Classification: 52A20, 52A27, 52A99, 52A41, 52B55
Citation: J. Math. Anal. Appl. 374:2 (2011), 529-537
Submitted from: dusan.repovs at guest.arnes.si
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1010.2320
or
http://arXiv.org/abs/1010.2320
From alspach at fourier.math.okstate.edu Fri Oct 29 17:43:08 2010
Return-Path: <alspach at fourier.math.okstate.edu>
X-Original-To: alspach
Delivered-To: alspach at fourier.math.okstate.edu
Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 26762D0E20; Fri, 29 Oct 2010 17:43:08 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Robert Cauty
Message-Id: <20101029224308.26762D0E20 at fourier.math.okstate.edu>
Date: Fri, 29 Oct 2010 17:43:08 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Points fixes des applications
compactes dans les espaces ULC" by Robert Cauty.
Abstract: A topological space is locally equiconnected if there exists
a neighborhood $U$ of the diagonal in $X\times X$ and a continuous
map $\lambda:U\times[0,1]\to X$ such that $\lambda(x,y,0)=x$,
$\lambda(x,y,1)=y$ et $\lambda(x,x,t)=x$ for $(x,y)\in U$ and $(x,t)\in
X\times[0,1]$. This class contains all ANRs, all locally contractible
topological groups and the open subsets of convex subsets of linear
topological spaces. In a series of papers, we extended the fixed point
theory of compact continuous maps, which was well developped for ANRs, to
all separeted locally equiconnected spaces. This generalization includes
a proof of Schauder's conjecture for compact maps of convex sets. This
paper is a survey of that work. The generalization has two steps: the
metrizable case, and the passage from the metrizable case to the general
case. The metrizable case is, by far, the most difficult. To treat this
case, we introduced in [4] the notion of algebraic ANR. Since the proof
that metrizable locally equiconnected spaces are algebraic ANRs is rather
difficult, we give here a detaled sketch of it in the case of a compact
convex subset of a metrizable t.v.s.. The passage from the metrizable
case to the general case uses a free functor and representations of
compact spaces as inverse limits of some special inverse systems of
metrizable compacta.
Archive classification: math.GN math.AT math.FA
Mathematics Subject Classification: 54C55
Submitted from: cauty at math.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1010.2401
or
http://arXiv.org/abs/1010.2401
From alspach at fourier.math.okstate.edu Fri Oct 29 17:45:06 2010
Return-Path: <alspach at fourier.math.okstate.edu>
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Received: by fourier.math.okstate.edu (Postfix, from userid 1005)
id 25B2FD0E20; Fri, 29 Oct 2010 17:45:06 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Isaac Goldbring
Message-Id: <20101029224506.25B2FD0E20 at fourier.math.okstate.edu>
Date: Fri, 29 Oct 2010 17:45:06 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Definable operators on Hilbert
spaces" by Isaac Goldbring.
Abstract: Let H be an infinite-dimensional (real or complex) Hilbert
space, viewed as a metric structure in its natural signature. We
characterize the definable linear operators on H as exactly the "scalar
plus compact" operators.
Archive classification: math.LO math.FA
Remarks: 10 pages
Submitted from: isaac at math.ucla.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1010.2243
or
http://arXiv.org/abs/1010.2243
From alspach at fourier.math.okstate.edu Fri Oct 29 17:46:25 2010
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id E7773D0E20; Fri, 29 Oct 2010 17:46:24 -0500 (CDT)
To: alspach at fourier.math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Tepper L Gill, Francis Mensah and Woodford W. Zachary
Message-Id: <20101029224624.E7773D0E20 at fourier.math.okstate.edu>
Date: Fri, 29 Oct 2010 17:46:24 -0500 (CDT)
From: alspach at fourier.math.okstate.edu (Dale Alspach)
Status: R
This is an announcement for the paper "Adjoint operators on Banach spaces"
by Tepper L Gill, Francis Mensah and Woodford W. Zachary.
Abstract: In this paper, we report on new results related to the
existence of an adjoint for operators on separable Banach spaces and
discuss a few interesting applications. (Some results are new even for
Hilbert spaces.) Our first two applications provide an extension of
the Poincar\'{e} inequality and the Stone-von Neumann version of the
spectral theorem for a large class of $C_0$-generators of contraction
semigroups on separable Banach spaces. Our third application provides a
natural extension of the Schatten-class of operators to all separable
Banach spaces. As a part of this program, we introduce a new class of
separable Banach spaces. As a side benefit, these spaces also provide a
natural framework for the (rigorous) construction of the path integral
as envisioned by Feynman.
Archive classification: math-ph math.FA math.MP
Mathematics Subject Classification: 46B03, 47D03, 47H06, 47F05, 35Q80
Submitted from: tgill at howard.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1010.4922
or
http://arXiv.org/abs/1010.4922
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Nov 2010 11:37:44 -0600 (CST)
Subject: Abstract of a paper by Nikolai Nikolski and Vasily Vasyunin
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Invertibility threshold for
$H^\infty$ trace algebras, and effective matrix inversions" by Nikolai
Nikolski and Vasily Vasyunin.
Abstract: For a given $\delta$, $0<\delta<1$, a
Blaschke sequence $\sigma=\{\lambda_j\}$ is constructed
such that every function $f$, $f\in H^\infty$, having
$\delta<\delta_f=\inf_{\lambda\in\sigma}|f(\lambda)|\le\|f\|_\infty\le1$
is invertible in the trace algebra $H^\infty|\sigma$ (with a norm estimate
of the inverse depending on $\delta_f$ only), but there exists $f$ with
$\delta=\delta_f\le\|f\|_\infty\le1$, which does not. As an application,
a counterexample to a stronger form of the Bourgain--Tzafriri restricted
invertibility conjecture for bounded operators is exhibited, where an
``orthogonal (or unconditional) basis'' is replaced by a ``summation
block orthogonal basis''.
Archive classification: math.FA
Submitted from: vasyunin at pdmi.ras.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1010.6090
or
http://arXiv.org/abs/1010.6090
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Jarno Talponen
Date: Tue, 23 Nov 2010 11:38:57 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Extracting long basic sequences
from systems of dispersed vectors" by Jarno Talponen.
Abstract: We study Banach spaces satisfying some geometric or
structural properties involving tightness of transfinite sequences of
nested linear subspaces. These properties are much weaker than WCG and
closely related to Corson's property (C). Given a transfinite sequence
of normalized vectors, which is dispersed or null in some sense, we
extract a subsequence which is a biorthogonal sequence, or even a weakly
null monotone basic sequence, depending on the setting. The Separable
Complementation Property is established for spaces with an M-basis under
rather weak geometric properties. We also consider an analogy of the
Baire Category Theorem for the lattice of closed linear subspaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B26, 46Bxx, 46M40
Remarks: 17 pages
Submitted from: talponen at cc.hut.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.0071
or
http://arXiv.org/abs/1011.0071
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Nov 2010 11:40:54 -0600 (CST)
Subject: Abstract of a paper by Jan Vybiral
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Average best $m$-term
approximation" by Jan Vybiral.
Abstract: We introduce the concept of average best $m$-term
approximation widths with respect to a probability measure on the unit
ball of $\ell_p^n$. We estimate these quantities for the embedding
$id:\ell_p^n\to\ell_q^n$ with $0<p\le q\le \infty$ for the normalized
cone and surface measure. Furthermore, we consider certain tensor product
weights and show that a typical vector with respect to such a measure
exhibits a strong compressible (i.e. nearly sparse) structure.
Archive classification: math.FA math.NA math.ST stat.TH
Mathematics Subject Classification: 41A46 (Primary) 46B20, 60B11
(Secondary)
Remarks: 2 figures
Submitted from: jan.vybiral at oeaw.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.0943
or
http://arXiv.org/abs/1011.0943
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Nov 2010 11:43:07 -0600 (CST)
Subject: Abstract of a paper by Olivier Guedon and Emanuel Milman
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Interpolating thin-shell and
sharp large-deviation estimates for isotropic log-concave measures"
by Olivier Guedon and Emanuel Milman.
Abstract: Given an isotropic random vector $X$ with log-concave density
in Euclidean space $\Real^n$, we study the concentration properties
of $|X|$. We show in particular that: \[ \P(|X| \geq (1+t) \sqrt{n})
\leq \exp(-c n^{\frac{1}{2}} \min(t^3,t)) \;\;\; \forall t > 0 ~,
\] for some universal constant $c>0$. This improves the best known
deviation results above the expectation on the thin-shell and mesoscopic
scales due to Fleury and Klartag, respectively, and recovers the sharp
large-deviation estimate of Paouris. Another new feature of our estimate
is that it improves when $X$ is $\psi_\alpha$ ($\alpha \in (1,2]$), in
precise agreement with the sharp Paouris estimates. The upper bound on
the thin-shell width $\sqrt{\Var(|X|)}$ we obtain is of the order of
$n^{1/3}$, and improves down to $n^{1/4}$ when $X$ is $\psi_2$. Our
estimates thus continuously interpolate between a new best known
thin-shell estimate and the sharp Paouris large-deviation one.
Archive classification: math.FA
Remarks: 23 pages
Submitted from: emanuel.milman at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.0943
or
http://arXiv.org/abs/1011.0943
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Nov 2010 11:48:30 -0600 (CST)
Subject: Abstract of a paper by Christian Le Merdy and Quanhua Xu
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Maximal theorems and square
functions for analytic operators on Lp-spaces" by Christian Le Merdy
and Quanhua Xu.
Abstract: Let T : Lp --> Lp be a contraction, with p strictly between
1 and infinity, and assume that T is analytic, that is, there exists a
constant K such that n\norm{T^n-T^{n-1}} < K for any positive integer
n. Under the assumption that T is positive (or contractively regular), we
establish the boundedness of various Littlewood-Paley square functions
associated with T. As a consequence we show maximal inequalities
of the form $\norm{\sup_{n\geq 0}\, (n+1)^m\bigl\vert T^n(T-I)^m(x)
\bigr\vert}_p\,\lesssim\, \norm{x}_p$, for any nonnegative integer
m. We prove similar results in the context of noncommutative Lp-spaces.
We also give analogs of these maximal inequalities for bounded analytic
semigroups, as well as applications to R-boundedness properties.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 47B38, 46L52, 46A60
Submitted from: clemerdy at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.1360
or
http://arXiv.org/abs/1011.1360
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Nov 2010 11:49:51 -0600 (CST)
Subject: Abstract of a paper by Joseph Lehec
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A direct proof of the functional
Santalo inequality" by Joseph Lehec.
Abstract: We give a simple proof of a functional version of the
Blaschke-Santalo inequality due to Artstein, Klartag and Milman. The proof
is by induction on the dimension and does not use the Blaschke-Santalo
inequality.
Archive classification: math.FA
Mathematics Subject Classification: 26D15 (52A40)
Citation: C. R. Math. Acad. Sci. Paris 347 (2009), no. 1-2, 55–58
Remarks: 4 pages, file might be slighlty diferent from the published
version
Submitted from: lehec at ceremade.dauphine.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.2140
or
http://arXiv.org/abs/1011.2140
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Nov 2010 11:51:52 -0600 (CST)
Subject: Abstract of a paper by Joseph Lehec
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the Yao-Yao partition theorem"
by Joseph Lehec.
Abstract: The Yao-Yao partition theorem states that given a probability
measure on an affine space of dimension n having a density which is
continuous and bounded away from 0, it is possible to partition the
space into 2^n regions of equal measure in such a way that every affine
hyperplane avoids at least one of the regions. We give a constructive
proof of this result and extend it to slightly more general measures.
Archive classification: math.FA math.CO
Mathematics Subject Classification: 52C99
Citation: Arch. Math. 92 (4) (2009) 366-376
Remarks: 10 pages, file might be slightly different from the published
version
Submitted from: lehec at ceremade.dauphine.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.2123
or
http://arXiv.org/abs/1011.2123
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Nov 2010 11:53:20 -0600 (CST)
Subject: Abstract of a paper by Joseph Lehec
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The symmetric property tau for
the Gaussian measure" by Joseph Lehec.
Abstract: We give a proof based on the Poincar\'e inequality of the
symmetric property tau for the Gaussian measure. This property turns out
to be equivalent to a certain functional form of the Blaschke-Santal\'o
inequality, as explained in a paper by Artstein, Klartag and Milman.
Archive classification: math.FA
Mathematics Subject Classification: 60D05 (28A75 52A39 52A40)
Citation: Ann. Fac. Sci. Toulouse Math. (6) 17 (2008), no. 2, 357–370
Remarks: 10 pages, file might be slightly different from the published
version
Submitted from: lehec at ceremade.dauphine.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.2142
or
http://arXiv.org/abs/1011.2142
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Nov 2010 11:54:45 -0600 (CST)
Subject: Abstract of a paper by Jan-David Hardtke
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Rainwater-Simons-type convergence
theorems for generalized convergence methods" by Jan-David Hardtke.
Abstract: We extend the well-known Rainwater-Simons convergence theorem to
various generalized convergence methods such as strong matrix summability,
statistical convergence and almost convergence. In fact we prove these
theorems not only for boundaries but for the more general notion of
(I)-generating sets introduced by Fonf and Lindenstrauss.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 40C05, 40C99
Remarks: 11 pages
Submitted from: hardtke at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.2365
or
http://arXiv.org/abs/1011.2365
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Nov 2010 11:56:09 -0600 (CST)
Subject: Abstract of a paper by Jan-David Hardtke
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some remarks on stronger versions
of the Boundary Problem for Banach spaces" by Jan-David Hardtke.
Abstract: Let $X$ be a real Banach space. A subset $B$ of the dual unit
sphere of $X$ is said to be a boundary for $X$, if every element of $X$
attains its norm on some functional in $B$. The well-known Boundary
Problem originally posed by Godefroy asks whether a bounded subset of
$X$ which is compact in the topology of pointwise convergence on $B$ is
already weakly compact. This problem was recently solved by H.Pfitzner
in the positive. In this note we collect some stronger versions of
the solution to the Boundary Problem, most of which are restricted to
special types of Banach spaces. We shall use the results and techniques
of Pfitzner, Cascales et al., Moors and others.
Archive classification: math.FA
Mathematics Subject Classification: 46A50, 46B50
Remarks: 14 pages
Submitted from: hardtke at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.2372
or
http://arXiv.org/abs/1011.2372
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Nov 2010 12:02:21 -0600 (CST)
Subject: Abstract of a paper by Dale E. Alspach and Eloi Medina Galego
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Geometry of the Banach spaces
C(beta mathbb N times K, l_p) for compact metric spaces K" by Dale
E. Alspach and Eloi Medina Galego .
Abstract: In this paper we provide the complete isomorphic classification
of the spaces C(beta mathbb N times K, l_p) of all continuous l_p-valued
functions, 1 <= p < infinity, defined on the topological product of
the Stone-Cech compactification of the natural numbers mathbb N and an
arbitrary infinite compact metric space K.
In order to do this, we first prove that c_0 is the only infinite
dimensional
separable C(K) space, Z, up to an isomorphism, which satisfies each one
of the following statements:
(1) Z is a quotient of C(beta mathbb N, l_p) for every 1< p< infinity.
(2) Z is isomorphic to a complemented subspace of C(beta mathbb N,
l_1). (3) C(beta mathbb N, l_p) is isomorphic to the injective tensor
product of
itself and Z, for every 1 <= p < infinity.
Archive classification: math.FA
Mathematics Subject Classification: 46B
Remarks: 17 pages
Submitted from: alspach at math.okstate.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.3261
or
http://arXiv.org/abs/1011.3261
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Nov 2010 12:05:42 -0600 (CST)
Subject: Abstract of a paper by D. Azagra, R. Fry and L. Keener
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Approximation of functions
and their derivatives by analytic maps on certain Banach spaces"
by D. Azagra, R. Fry and L. Keener.
Abstract: Let X be a separable Banach space which admits a separating
polynomial; in particular X a separable Hilbert space. Let f:X→R be
bounded, Lipschitz, and C¹ with uniformly continuous derivative. Then
for each {\epsilon}>0, there exists an analytic function g:X→R with
|g-f|<{\epsilon} and ‖g′-f′‖<{\epsilon}.
Archive classification: math.FA
Remarks: 17 pages
Submitted from: rfry at tru.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.4613
or
http://arXiv.org/abs/1011.4613
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Nov 2010 12:07:05 -0600 (CST)
Subject: Abstract of a paper by Matthew Tarbard
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Hereditarily indecomposable,
separable L_\infty spaces with \ell_1 dual having few operators,
but not very few operators" by Matthew Tarbard.
Abstract: Given a natural number $k \geq 2$, we construct a hereditarily
indecomposable, $\mathscr{L}_{\infty}$ space, $X_k$ with dual isomorphic
to $\ell_1$. We exhibit a non-compact, strictly singular operator $S$
on $X_k$, with the property that $S^k = 0$ and $S^j (0 \leq j \leq k-1)$
is not a compact perturbation of any linear combination of $S^l, l \neq
j$. Moreover, every bounded linear operator on this space has the form
$\sum_{i=0}^{k-1} \lambda_i S^i +K$ where the $\lambda_i$ are scalars
and $K$ is compact. In particular, this construction answers a question
of Argyros and Haydon ( "A hereditarily indecomposable space that solves
the scalar-plus-compact problem").
Archive classification: math.FA
Submitted from: matthew.tarbard at sjc.ox.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.4776
or
http://arXiv.org/abs/1011.4776
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Nov 2010 12:08:30 -0600 (CST)
Subject: Abstract of a paper by Miguel Martin, Javier Meri and Mikhail
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the numerical radius of
operators in Lebesgue spaces" by Miguel Martin, Javier Meri and Mikhail
Popov.
Abstract: We show that the absolute numerical index of the space
$L_p(\mu)$ is $p^{-\frac{1}{p}} q^{-\frac{1}{q}}$ (where $1/p+1/q=1$). In
other words, we prove that $$ \sup\left\{\int |x|^{p-1}|Tx|\, d\mu
\, : \ x\in L_p(\mu),\,\|x\|_p=1\right\} \,\geq \,p^{-\frac{1}{p}}
q^{-\frac{1}{q}}\,\|T\| $$ for every $T\in \mathcal{L}(L_p(\mu))$ and that
this inequality is the best possible when the dimension of $L_p(\mu)$
is greater than one. We also give lower bounds for the best constant
of equivalence between the numerical radius and the operator norm in
$L_p(\mu)$ for atomless $\mu$ when restricting to rank-one operators or
narrow operators.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 46B20, 47A12
Remarks: 14 pages
Submitted from: mmartins at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.4785
or
http://arXiv.org/abs/1011.4785
Return-path: <alspach at math.okstate.edu>
From: Dale Alspach <alspach at math.okstate.edu>
Date: Fri, 10 Dec 2010 08:51:46 -0600
To: banach at math.okstate.edu
Announcement of Meeting:
SET THEORETIC TECHNIQUES IN FUNCTIONAL ANALYSIS
To be held in Castro Urdiales (Cantabria) Spain,
from February 21 to February 24, 2011.
Organized by Jesús M. F. Castillo (Univ. of Extremadura) and
Manuel González (Univ. of Cantabria), in collaboration with
the CIEM (International Center for Matematical Encounters).
The meeting includes six mini-courses lectured by:
Antonio Avilés (Univ. Murcia, Spain) (2 hours)
Push-out constructions in Banach spaces and Boolean algebras
Valentin Ferenczi (Univ. Sao Paulo, Brasil) (2 hours)
Groups of isometries on Banach spaces
Piotr Koszmider (Univ. Lodz, Poland) (2 hours)
Some applications of set-theoretic topological methods in C(K) spaces
Wieslaw Kubis (Univ. Praga, Czech Republic) (2 hours)
Category-theoretic methods for constructing universal Banach spaces
Jordi López Abad (ICMAT-CSIC, Madrid, Spain) (2 hours)
Banach Spaces and Ramsey Theory: some open problems
Stevo Todorcevic (Univ. Toronto, Canada) (3 hours)
Combinatorial dichotomies in set theory and their applications to analysis
Participants will have the possibility of delivering short lectures
of 20 or 30 minutes.
Registration for the meeting can be done through the web-site:
http://www.ciem.unican.es/encuentros/banach2011.
There is no registration fee.
Additional information can be found in that web-site.
The meeting is supported by CIEM, Universidad de Cantabria,
Ayuntamiento de Castro Urdiales and Ingenio Mathematica.
Antonio MArtínez-Abejón (University of Oviedo, Spain)
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 21 Dec 2010 13:36:37 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Gustavo Corach and Alejandra Maestripieri
This is an announcement for the paper "Products of orthogonal projections
and polar decompositions" by Gustavo Corach and Alejandra Maestripieri.
Abstract: We characterize the sets $\XX$ of all products $PQ$, and $\YY$
of all products $PQP$, where $P,Q$ run over all orthogonal projections and
we solve the problems \newline $\arg\min\{\|P-Q\|: (P,Q) \in \cal Z\}$,
for $\cal Z=\XX$ or $\YY.$ We also determine the polar decompositions
and Moore-Penrose pseudoinverses of elements of $\XX.$
Archive classification: math.FA
Mathematics Subject Classification: 47A05
Submitted from: gcorach at fi.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.5237
or
http://arXiv.org/abs/1011.5237
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 21 Dec 2010 13:39:17 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by O.F.K. Kalenda, H. Pfitzner and J. Spurny
This is an announcement for the paper "On quantification of weak
sequential completeness" by O.F.K. Kalenda, H. Pfitzner and J. Spurny.
Abstract: We consider several quantities related to weak sequential
completeness of a Banach space and prove some of their properties in
general and in $L$-embedded Banach spaces, improving in particular an
inequality of G.~Godefroy, N.~Kalton and D.~Li. We show some examples
witnessing natural limits of our positive results, in particular,
we construct a separable Banach space $X$ with the Schur property
that cannot be renormed to have a certain quantitative form of weak
sequential completeness, thus providing a partial answer to a question
of G.~Godefroy.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 9 pages
Submitted from: kalenda at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.6553
or
http://arXiv.org/abs/1011.6553
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 21 Dec 2010 13:45:39 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Rafal Latala
This is an announcement for the paper "Order statistics and concentration
of l_r norms for log-concave vectors" by Rafal Latala.
Abstract: We establish upper bounds for tails of order statistics of
isotropic log-concave vectors and apply them to derive a concentration
of l_r norms of such vectors.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 60E15 (52A38, 60B11)
Remarks: 17 pages
Submitted from: rlatala at mimuw.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.6610
or
http://arXiv.org/abs/1011.6610
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 21 Dec 2010 13:48:27 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
Subject: Abstract of a paper by Radoslaw Adamczak, Alexander E. Litvak, Alain Pajor, and Nicole Tomczak-Jaegermann
This is an announcement for the paper "Sharp bounds on the rate of
convergence of the empirical covariance matrix" by Radoslaw Adamczak,
Alexander E. Litvak, Alain Pajor, and Nicole Tomczak-Jaegermann.
Abstract: Let $X_1,..., X_N\in\R^n$ be independent centered random
vectors with log-concave distribution and with the identity as covariance
matrix. We show that with overwhelming probability at least $1 - 3
\exp(-c\sqrt{n}\r)$ one has $
\sup_{x\in S^{n-1}} \Big|\frac{1/N}\sum_{i=1}^N (|<X_i, x>|^2 - \E|<X_i,
x>|^2\r)\Big|
\leq C \sqrt{\frac{n/N}},$ where $C$ is an absolute positive
constant. This
result is valid in a more general framework when the linear forms
$(<X_i,x>)_{i\leq N, x\in S^{n-1}}$ and the Euclidean norms $(|X_i|/\sqrt
n)_{i\leq N}$ exhibit uniformly a sub-exponential decay. As a consequence,
if $A$ denotes the random matrix with columns $(X_i)$, then with
overwhelming probability, the extremal singular values $\lambda_{\rm
min}$ and $\lambda_{\rm max}$ of $AA^\top$ satisfy the inequalities $ 1 -
C\sqrt{{n/N}} \le {\lambda_{\rm min}/N} \le \frac{\lambda_{\rm max}/N}
\le 1 + C\sqrt{{n/N}} $ which is a quantitative version of Bai-Yin
theorem \cite{BY} known for random matrices with i.i.d. entries.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 52A20, 46B09, 52A21 (Primary) 15A52,
60E15 (Secondary)
Submitted from: radamcz at mimuw.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1012.0294
or
http://arXiv.org/abs/1012.0294
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Taras Banakh and Arkady Leiderman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 21 Dec 2010 13:56:37 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Uniform Eberlein compactifications
of metrizable spaces" by Taras Banakh and Arkady Leiderman.
Abstract: We prove that each metrizable space (of cardinality less
or equal to continuum) has a (first countable) uniform Eberlein
compactification and each scattered metrizable space has a scattered
hereditarily paracompact compactification. Each compact scattered
hereditarily paracompact space is uniform Eberlein and belongs to
the smallest class of compact spaces, that contain the empty set, the
singleton, and is closed under producing the Aleksandrov compactification
of the topological sum of a family of compacta from that class.
Archive classification: math.GN math.FA
Mathematics Subject Classification: 54D35, 54G12, 54D30, 54D20
Remarks: 6 pages
Submitted from: tbanakh at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1012.0920
or
http://arXiv.org/abs/1012.0920
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Rafal Latala
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 21 Dec 2010 14:05:04 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Weak and strong moments of random
vectors" by Rafal Latala.
Abstract: We discuss a conjecture about comparability of weak and strong
moments of log-concave random vectors and show the conjectured inequality
for unconditional vectors in normed spaces with a bounded cotype constant.
Archive classification: math.PR math.FA
Mathematics Subject Classification: Primary 60E15, Secondary 52A40, 60B11
Remarks: 8 pages
Submitted from: rlatala at mimuw.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1012.2703
or
http://arXiv.org/abs/1012.2703
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Spiros A. Argyros and Giorgos Petsoulas
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 21 Dec 2010 14:11:56 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A $c_0$ saturated Banach space
with tight structure" by Spiros A. Argyros and Giorgos Petsoulas.
Abstract: It is shown that variants of the HI methods could yield objects
closely connected to the classical Banach spaces. Thus we present a new
$c_0$ saturated space, denoted as $\mathfrak{X}_0$, with rather tight
structure. The space $\mathfrak{X}_0$ is not embedded into a space with
an unconditional basis and its complemented subspaces have the following
structure. Everyone is either of type I, namely, contains an isomorph of
$\mathfrak{X}_0$ itself or else is isomorphic to a subspace of $c_0$ (type
II). Furthermore for any analytic decomposition of $\mathfrak{X}_0$ into
two subspaces one is of type I and the other is of type II. The operators
of $\mathfrak{X}_0$ share common features with those of HI spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B26
Remarks: 24 pages
Submitted from: sargyros at math.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1012.2758
or
http://arXiv.org/abs/1012.2758
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by D. Azagra, R. Fry, and L. Keener
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 21 Dec 2010 14:13:32 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Real analytic approximations
which almost preserve Lipschitz constants of functions defined on the
Hilbert space" by D. Azagra, R. Fry, and L. Keener.
Abstract: Let $X$ be a separable real Hilbert space. We show that for
every Lipschitz function $f:X\rightarrow\mathbb{R}$, and for every
$\varepsilon>0$, there exists a Lipschitz, real analytic function
$g:X\rightarrow\mathbb{R}$ such that $|f(x)-g(x)|\leq \varepsilon$
and $\textrm{Lip}(g)\leq \textrm{Lip}(f)+\varepsilon$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 7 pages
Submitted from: dazagra at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1012.4339
or
http://arXiv.org/abs/1012.4339
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Rodrigo Banuelos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 30 Dec 2010 15:30:03 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The foundational inequalities of
D.L. Burkholder and some of their ramifications" by Rodrigo Banuelos.
Abstract: This paper present an overview of some of the applications of
the martingale transform inequalities of D.L.~Burkholder to $L^p$-bounds
for singular integrals concentrating on $L^p$-bounds for the Hilbert,
Riesz, Beurling-Ahlfors transforms and other multipliers obtained by
projections (conditional expectations) of transformations of stochastic
integrals. The aim is to obtain optimal, or near optimal, bounds in
these inequalities.
Connections to other areas of mathematics where these inequalities
and the techniques to prove them have become of considerable interest
in recent years, are also discussed.
Archive classification: math.PR math.AP math.FA
Submitted from: banuelos at math.purdue.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1012.4850
or
http://arXiv.org/abs/1012.4850
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Rodrigo Banuelos and Burgess Davis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 30 Dec 2010 15:31:20 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Donald Burkholder's work in
martingales and analysis" by Rodrigo Banuelos and Burgess Davis.
Abstract: Overview of Burkholder's work on martingales and analysis
Archive classification: math.PR math.FA
Submitted from: banuelos at math.purdue.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1012.4849
or
http://arXiv.org/abs/1012.4849
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio Aviles and Christina Brech
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 30 Dec 2010 15:32:44 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A Boolean algebra and a Banach
space obtained by push-out iteration" by Antonio Aviles and Christina
Brech.
Abstract: Under the assumption that the continuum c is a regular cardinal,
we prove the existence and uniqueness of a Boolean algebra B of size
c defined by sharing the main structural properties that P(N)/fin has
under CH and in the aleph2-Cohen model. We prove a similar result in
the category of Banach spaces.
Archive classification: math.LO math.CT math.FA
Mathematics Subject Classification: 06E05, 03E35, 03G05, 46B26, 54G05,
18A30
Submitted from: avileslo at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1012.5051
or
http://arXiv.org/abs/1012.5051
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio Aviles
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 30 Dec 2010 15:34:18 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Radon-Nikodym compact spaces of
low weight and Banach spaces" by Antonio Aviles.
Abstract: We prove that a continuous image of a Radon-Nikod\'{y}m
compact space of weight less than b is Radon-Nikod\'{y}m compact. As a
Banach space counterpart, subspaces of Asplund generated Banach spaces
of density character less than b are Asplund generated. In this case,
in addition, there exists a subspace of an Asplund generated space which
is not Asplund generated which has density character exactly b.
Archive classification: math.FA math.GN
Mathematics Subject Classification: Primary 46B26, Secondary 46B22,
46B50, 54G99
Citation: Studia Math. 166 (2005), no. 1, 71–82
Submitted from: avileslo at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1012.5512
or
http://arXiv.org/abs/1012.5512
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jose Orihuela, Richard J. Smith, and
Stanimir Troyanski
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 30 Dec 2010 15:35:42 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Strictly convex norms and topology"
by Jose Orihuela, Richard J. Smith, and Stanimir Troyanski.
Abstract: We introduce a new topological property called (*) and the
corresponding class of topological spaces, which includes spaces with
$G_\delta$-diagonals and Gruenhage spaces. Using (*), we characterise
those Banach spaces which admit equivalent strictly convex norms, and
give an internal topological characterisation of those scattered compact
spaces $K$, for which the dual Banach space $C(K)^*$ admits an equivalent
strictly convex dual norm. We establish some relationships between (*)
and other topological concepts, and the position of several well-known
examples in this context. For instance, we show that $C(\mathcal{K})^*$
admits an equivalent strictly convex dual norm, where $\mathcal{K}$
is Kunen's compact space. Also, under the continuum hypothesis CH,
we give an example of a compact scattered non-Gruenhage space having (*).
Archive classification: math.FA math.GN
Submitted from: richard.smith at ucd.ie
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1012.5595
or
http://arXiv.org/abs/1012.5595
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Orest Bucicovschi and Jiri Lebl
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 30 Dec 2010 15:36:55 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the continuity and regularity
of convex extensions" by Orest Bucicovschi and Jiri Lebl.
Abstract: We study continuity and regularity of convex extensions of
functions from a compact set $C$ to its convex hull $K$. We show that
if $C$ contains the relative boundary of $K$, and $f$ is a continuous
convex function on $C$, then $f$ extends to a continuous convex function
on $K$ using the standard convex roof construction. In fact, a necessary
and sufficient condition for $f$ to extend from any set to a continuous
convex function on the convex hull is that $f$ extends to a continuous
convex function on the relative boundary of the convex hull. We give
examples showing that the hypotheses in the results are necessary. In
particular, if $C$ does not contain the entire relative boundary of
$K$, then there may not exist any continuous convex extension of $f$.
Finally, when $\partial K$ and $f$ are $C^1$ we give a necessary and
sufficient condition for the convex roof construction to be $C^1$ on all
of $K$. We also discuss an application of the convex roof construction
in quantum computation.
Archive classification: math.FA
Mathematics Subject Classification: 52A41, 81P68
Remarks: 12 pages, 2 figures
Submitted from: jlebl at math.ucsd.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1012.5796
or
http://arXiv.org/abs/1012.5796
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mark W. Meckes
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 30 Dec 2010 15:40:13 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Positive definite metric spaces"
by Mark W. Meckes.
Abstract: Magnitude is a numerical invariant of finite metric spaces,
recently introduced by T.\ Leinster, which is analogous in precise
senses to the cardinality of finite sets or the Euler characteristic of
topological spaces. It has been extended to infinite metric spaces in
several a priori distinct ways. This paper develops the theory of a class
of metric spaces, positive definite metric spaces, for which magnitude
is more tractable than in general. In particular, it is shown that all
the proposed definitions of magnitude coincide for compact positive
definite metric spaces. Some additional results are proved about the
behavior of magnitude as a function of such spaces, and a number of
examples of positive definite metric spaces are found, including all
subsets of $L_p$ for $p\le 2$ and Euclidean spheres equipped with the
geodesic distance. Finally, some facts about the magnitude of compact
subsets of $\ell_p^n$ for $p \le 2$ are proved, generalizing results of
Leinster for $p=1,2$, using properties of these spaces which are somewhat
stronger than positive definiteness.
Archive classification: math.MG math.FA math.GN
Submitted from: mark.meckes at case.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1012.5863
or
http://arXiv.org/abs/1012.5863
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