Banach October 2012

banach@mathdept.okstate.edu

1 participants
14 discussions

Abstract of a paper by E.Ostrovsky and L.Sirota
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "A Banach rearrangement norm characterization for tail behavior of measurable functions (random variables)" by E.Ostrovsky and L.Sirota. Abstract: We construct a Banach rearrangement invariant norm on the measurable space for which the finiteness of this norm for measurable function (random variable) is equivalent to suitable tail (heavy tail and light tail) behavior. We investigate also a conjugate to offered spaces and obtain some embedding theorems. Possible applications: Functional Analysis (for instance, interpolation of operators), Integral Equations, Probability Theory and Statistics (tail estimations for random variables). Archive classification: math.FA math.PR Submitted from: leos(a)post.sce.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.1168 or http://arXiv.org/abs/1210.1168

1 0

Abstract of a paper by Jan-David Hardtke
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "On convergence with respect to an ideal and a family of matrices" by Jan-David Hardtke. Abstract: Recently P. Das, S. Dutta and E. Savas introduced and studied the notions of strong $A^I$-summability with respect to an Orlicz function $F$ and $A^I$-statistical convergence, where $A$ is a non-negative regular matrix and $I$ is an ideal on the set of natural numbers. In this note, we will generalise these notions by replacing $A$ with a family of matrices and $F$ with a family of Orlicz functions or moduli and study the thus obtained convergence methods. We will also give an application in Banach space theory, presenting a generalisation of Simons' $\sup$-$\limsup$-theorem to the newly introduced convergence methods (for the case that the filter generated by the ideal $I$ has a countable base), continuing the author's previous work. Archive classification: math.FA Mathematics Subject Classification: 40C05, 40C99, 46B20 Remarks: 32 pages Submitted from: hardtke(a)math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.1350 or http://arXiv.org/abs/1210.1350

1 0

Abstract of a paper by Costas Poulios
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "Non-separable tree-like Banach spaces and Rosenthal's $\ell_1$-theorem " by Costas Poulios. Abstract: We introduce and investigate a class of non-separable tree-like Banach spaces. As a consequence, we prove that we can not achieve a satisfactory extension of Rosenthal's $\ell_1$-theorem to spaces of the type $\ell_1(\kappa)$, for $\kappa$ an uncountable cardinal. Archive classification: math.FA Mathematics Subject Classification: 46B25, 46B26 Submitted from: k-poulios(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.0792 or http://arXiv.org/abs/1210.0792

1 0

Abstract of a paper by Florent P. Baudier
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "Quantitative nonlinear embeddings into Lebesgue sequence spaces" by Florent P. Baudier. Abstract: In this paper coarse, uniform and strong embeddings of metric spaces into Lebesgue sequence spaces are studied in their quantitative aspects. In particular, strong deformation gaps are obtained when embedding strongly a Hilbert space into $\ell_p$ for $0<p< 2$ as well as new insights on the nonlinear geometry of the spaces $L_p$ and $\ell_p$ for $0<p<1$. The exact $\ell_q$-compression of $\ell_p$-spaces is computed. Finally the coarse deformation of metric spaces with property A and amenable groups is investigated. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B20, 46B85, 46T99, 20F65 Submitted from: florent(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.0588 or http://arXiv.org/abs/1210.0588

1 0

2025

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

Banach October 2012