Weak compactness in the dual of a \(C^*\)-algebra is determined commutatively
type: Item
instance of: scholarly article
title: Weak compactness in the dual of a \(C^*\)-algebra is determined commutatively
zbMATH Open document ID: 0791.46035
DOI: 10.1007/BF01459739
published in: Mathematische Annalen
publication date: 1994-03-23T00:00:00Z
full work available at URL: https://eudml.org/doc/165175
review text: We prove Pelczyński's property (V) for \(C^*\)-algebras by proving that weak compactness in the dual of a \(C^*\)-algebra is determined commutatively. Thus von Neumann algebras -- and in particular \(L(H)\) -- are Grothendieck spaces.
Mathematics Subject Classification ID: 46L10
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 537321
zbMATH Keywords: Pelczyński's property (V) for \(C^*\)-algebras
zbMATH Keywords: weak compactness in the dual of a \(C^*\)-algebra is determined commutatively
zbMATH Keywords: Grothendieck spaces
author: Hermann Pfitzner
reviewed by: Hermann Pfitzner
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 537321