The convex point of continuity property in Asplund spaces
type: Item
instance of: scholarly article
title: The convex point of continuity property in Asplund spaces
zbMATH Open document ID: 0944.46008
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-09-14T00:00:00Z
review text: A Banach space has the convex point of continuity property (CPCP) if, for every non-empty closed convex subset \(D\) of the unit ball, the identity map on \(D\) has a point of weak-to-norm continuity. The author shows that if \(X\) is an Asplund space then the following are equivalent: \(X\) has the CPCP; each subspace of \(X\) with a basis has the CPCP; each subspace of \(X\) with a shrinking basis has the CPCP.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B22
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 1384922
zbMATH Keywords: convex point of continuity property
zbMATH Keywords: Asplund spaces
zbMATH Keywords: point of weak-to-norm continuity
zbMATH Keywords: basis
zbMATH Keywords: Radon-Nikodym property
zbMATH Keywords: shrinking basis
author: Ginés López-Pérez
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6553
OpenAlex ID: W2034813392
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DOI: 10.1006/JMAA.1999.6553
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description: scientific article; zbMATH DE number 1384922