Banach May 2007

banach@mathdept.okstate.edu

2 participants
5 discussions

Abstract of a paper by S.S. Kutateladze
by Dale Alspach 30 May '07

30 May '07

This is an announcement for the paper "Interaction of order and convexity" by S.S. Kutateladze. Abstract: This is an overview of merging the techniques of Riesz space theory and convex geometry. Archive classification: math.FA Mathematics Subject Classification: 46B42; 52A39 Remarks: Prepared for the Russian--German geometry meeting dedicated to the The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/ or http://arXiv.org/abs/ or by email in unzipped form by transmitting an empty message with subject line uget or in gzipped form by using subject line get to: math(a)arXiv.org.

1 0

Abstract of a paper by Han Ju Lee
by Dale Alspach 19 May '07

19 May '07

This is an announcement for the paper "Strong peak points and denseness of strong peak functions" by Han Ju Lee. Abstract: Let $C_b(K)$ be the set of all bounded continuous (real or complex) functions on a complete metric space $K$ and $A$ a closed subspace of $C_b(K)$. Using the variational method, it is shown that the set of all strong peak functions in $A$ is dense if and only if the set of all strong peak points is a norming subset of $A$. As a corollary we show that if $X$ is a locally uniformly convex, complex Banach space, then the set of all strong peak functions in $\mathcal{A}(B_X)$ is a dense $G_\delta$ subset. Moreover if $X$ is separable, smooth and locally uniformly convex, then the set of all norm and numerical strong peak functions in $\mathcal{A}_u(B_X:X)$ is a dense $G_\delta$ subset. In case that a set of uniformly strongly exposed points of a (real or complex) Banach space $X$ is a norming subset of $\mathcal{P}({}^n X)$ for some $n\ge 1$, then the set of all strongly norm attaining elements in $\mathcal{P}({}^n X)$ is dense, in particular, the set of all points at which the norm of $\mathcal{P}({}^n X)$ is Fr\'echet differentiable is a dense $G_\delta$ subset. Archive classification: math.FA Mathematics Subject Classification: 46B04, 46G20, 46G25, 46B22 The source file(s), variationalmethod-2007-04-15.tex: 25864 bytes, is(are) stored in gzipped form as 0705.2650.gz with size 8kb. The corresponding postcript file has gzipped size 75kb. Submitted from: hahnju(a)postech.ac.kr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0705.2650 or http://arXiv.org/abs/0705.2650 or by email in unzipped form by transmitting an empty message with subject line uget 0705.2650 or in gzipped form by using subject line get 0705.2650 to: math(a)arXiv.org.

1 0

Abstract of a paper by Jarno Talponen
by Dale Alspach 19 May '07

19 May '07

This is an announcement for the paper "Convex-transitive characterizations of Hilbert spaces" by Jarno Talponen. Abstract: In this paper we investigate real convex-transitive Banach spaces X, which admit a 1-dimensional bicontractive projection P on X. Various mild conditions regarding the weak topology and the geometry of the norm are provided, which guarantee that such an X is in fact isometrically a Hilbert space. The results obtained can be regarded as partial answers to the well-known Banach-Mazur rotation problem, as well as to a question posed by B. Randrianantoanina in 2002 about convex-transitive spaces. Archive classification: math.FA Mathematics Subject Classification: 46B04; 46C15 The source file(s), amsct2.tex: 89202 bytes, is(are) stored in gzipped form as 0705.2526.gz with size 24kb. The corresponding postcript file has gzipped size 142kb. Submitted from: talponen(a)cc.helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0705.2526 or http://arXiv.org/abs/0705.2526 or by email in unzipped form by transmitting an empty message with subject line uget 0705.2526 or in gzipped form by using subject line get 0705.2526 to: math(a)arXiv.org.

1 0

History of Banach Spaces and Linear Operators
by Dale Alspach 03 May '07

03 May '07

This is an announcement of the publication of the book History of Banach Spaces and Linear Operators by Albrecht Pietsch The table of contents and preface can be viewed here: http://www.math.okstate.edu/~alspach/banach/pietsch-history.pdf

1 0

Abstract of a paper by Daniel Freeman
by Dale Alspach 03 May '07

03 May '07

This is an announcement for the paper "Weakly null sequences with upper estimates" by Daniel Freeman. Abstract: We prove that if $(v_i)$ is a normalized basic sequence and X is a Banach space such that every normalized weakly null sequence in X has a subsequence that is dominated by $(v_i)$, then there exists a uniform constant $C\geq1$ such that every normalized weakly null sequence in X has a subsequence that is C-dominated by $(v_i)$. This extends a result of Knaust and Odell, who proved this for the cases in which $(v_i)$ is the standard basis for $\ell_p$ or $c_0$. Archive classification: math.FA Mathematics Subject Classification: 46B20; 46B03, 46B10 Remarks: 21 pages The source file(s), FreemanUpEst.tex, is(are) stored in gzipped form as 0705.0218.gz with size 20kb. The corresponding postcript file has gzipped size 146kb. Submitted from: freeman(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0705.0218 or http://arXiv.org/abs/0705.0218 or by email in unzipped form by transmitting an empty message with subject line uget 0705.0218 or in gzipped form by using subject line get 0705.0218 to: math(a)arXiv.org.

1 0

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

Banach May 2007