A note on the intersection of Banach subspaces
type: Item
instance of: scholarly article
title: A note on the intersection of Banach subspaces
zbMATH Open document ID: 1071.46017
author: Yanyan Li
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2004-11-01T00:00:00Z
review text: In this article, the authors prove that a Banach space \(X\) is reflexive if and only if, for every \(x \in X\) and every decreasing sequence \((X_n)\) of closed subspaces of \(X\), \(d(x,\bigcap_{n=1}^\infty X_n) = \lim_{n\to\infty} d(x,X_n)\) where \(d(x,C)\) denotes the distance from \(x\) to \(C\).
reviewed by: B. Turett
Mathematics Subject Classification ID: 46B10
Mathematics Subject Classification ID: 46B03
zbMATH DE Number: 2113000
zbMATH Keywords: reflexive
zbMATH Keywords: Banach space
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1145475964
OpenAlex ID: W1995077258
cites work: Functional analysis and infinite-dimensional geometry
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cites work: Reflexivity and the supremum of linear functionals
cites work: Characterizations of reflexivity
cites work: Q5800527
cites work: Q4136031
cites work: Q5890171
cites work: Q5595759
DOI: 10.2977/PRIMS/1145475964
description: scientific article; zbMATH DE number 2113000