Weakly open sets in the unit ball of some Banach spaces and the centralizer
type: Item
instance of: scholarly article
title: Weakly open sets in the unit ball of some Banach spaces and the centralizer
zbMATH Open document ID: 1206.46012
author: María D. Acosta
author: Julio Becerra-Guerrero
published in: Journal of Functional Analysis
publication date: 2010-07-19T00:00:00Z
review text: This paper adds to the knowledge of spaces in which every nonempty weakly open subset of the unit ball is of norm diameter 2. In this substantial contribution, the authors show that for any Banach space \(X\) with an infinite-dimensional centralizer, for any positive integer \(N\), the \(N\)-fold symmetric projective tensor product of \(X\), endowed with the symmetric projective norm, has this property. They also show that when \(X\) is non-reflexive with \(X^\ast\) \(L\)-embedded, the space generated by the duals of \(X\) of even order has an infinite-dimensional centralizer.
Mathematics Subject Classification ID: 46B04
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 46G25
zbMATH DE Number: 5757613
zbMATH Keywords: symmetric projective tensor products
zbMATH Keywords: weakly open sets
zbMATH Keywords: centralizer
zbMATH Keywords: Cunningham algebra
reviewed by: T.S.S.R.K. Rao
MaRDI profile type: Publication
full work available at URL: j.jfa.2010.03.014
OpenAlex ID: W1997452898
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DOI: 10.1016/J.JFA.2010.03.014
description: scientific article; zbMATH DE number 5757613