Norm-attaining operators into strictly convex Banach spaces
type: Item
instance of: scholarly article
title: Norm-attaining operators into strictly convex Banach spaces
zbMATH Open document ID: 0914.46013
author: Francisco J. Aguirre
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-11-03T00:00:00Z
review text: Bishop and Phelps proved in 1961 that the set of scalar valued norm attaining bounded linear operators on any Banach space \(X\) is dense in \(X^*\). The author considers here the problem of extending this result to one in which the scalar field is replaced by a more general Banach space \(Y\), showing that if \(Y\) is strictly convex and contains a certain type of basic sequence, then there exists a Banach space \(X\) for which the norm attaining operators from \(X\) to \(Y\) are not dense. A corollary is that no uniformly convex Banach space has Property B of Lindenstrauss.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 1218611
zbMATH Keywords: norm attaining bounded linear operators
zbMATH Keywords: strictly convex
reviewed by: James R. Holub
MaRDI profile type: Publication
full work available at URL: jmaa.1998.5913
OpenAlex ID: W2057945282
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DOI: 10.1006/JMAA.1998.5913
description: scientific article; zbMATH DE number 1218611