An extension of a structure theorem of Bourgain
type: Item
instance of: scholarly article
title: An extension of a structure theorem of Bourgain
zbMATH Open document ID: 0726.46010
DOI: 10.1016/0022-247X(90)90373-N
author: D. E. G. Hare
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: A Banach space X is said to have the Point-of-Continuity Property (PCP) if every bounded subset of X has relatively weakly open subsets of arbitrarily small diameter. If this is true for every bounded convex subset of X then X is said to have the Convex Point-of-Continuity Property (CPCP). The main result of this paper asserts that if X fails to have CPCP, then it contains a subspace Y which also does not have CPCP, but such that Y admits a finite dimensional decomposition. Similar results for Banach spaces X having the Radon-Nikodym property or PCP, were obtained by \textit{J. Bourgain}, Stud. Math. 67, 135-148 (1980; Zbl 0434.46017) and Publ. Math. Univ. Pierre et Marie Curie, No.36 (1979).
Mathematics Subject Classification ID: 46B22
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 4198800
zbMATH Keywords: Point-of-Continuity Property
zbMATH Keywords: PCP
zbMATH Keywords: Convex Point-of-Continuity Property
zbMATH Keywords: CPCP
zbMATH Keywords: finite dimensional decomposition
zbMATH Keywords: Radon-Nikodym property
reviewed by: Stefan Cobzaş
MaRDI profile type: Publication
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full work available at URL: 0022-247x(90)90373-n
OpenAlex ID: W2056971484
description: scientific article; zbMATH DE number 4198800