The Mazur property for compact sets
type: Item
instance of: scholarly article
title: The Mazur property for compact sets
zbMATH Open document ID: 0653.46021
author: Abderrazzak Sersouri
published in: Pacific Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The author establishes the following smoothness property. Let X be a Banach space. Every compact convex set of X is the intersection of balls containing it if and only if the cone of the extreme points of the dual X' is dense in X' with respect to the topology of uniform convergence on compact sets of X. This characterization is also used to derive other results and applications as stability under \(c_ 0\) and \(\ell_ p\) sums, \(1\leq p<\infty\), and renorming theorems. Some of the author's proofs unify and simplify previous proof techniques.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46A50
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 4065670
zbMATH Keywords: Mazur property
zbMATH Keywords: transfinite Schauder bases
zbMATH Keywords: smoothness property
zbMATH Keywords: compact convex set
zbMATH Keywords: extreme points
zbMATH Keywords: topology of uniform convergence on compact sets
zbMATH Keywords: stability under \(c_ 0\) and \(\ell _ p\) sums
zbMATH Keywords: renorming theorems
reviewed by: Patrizia Pucci
MaRDI profile type: Publication
full work available at URL: pjm.1988.133.185
OpenAlex ID: W2084017583
DOI: 10.2140/PJM.1988.133.185
description: scientific article; zbMATH DE number 4065670