A variant of Grothendieck's theorem on weak* convergent sequences
type: Item
instance of: scholarly article
title: A variant of Grothendieck's theorem on weak* convergent sequences
zbMATH Open document ID: 0855.46018
DOI: 10.1007/BF01195095
author: Helmut H. Schaefer
author: Xiao-Dong Zhang
published in: Archiv der Mathematik
publication date: 1997-02-09T00:00:00Z
review text: The authors give a new proof of the following theorem: Let \(K\) be a compact quasi-Stonian space. Then every \(\sigma (C(K)^*, C(K))\)-compact subset of \(C(K)^*_c\) is also \(\sigma (C(K)^*, C(K)^{**})\)-compact. Hereby \(C(K)^*_c\) denotes the space of all sequentially order continuous linear functionals on \(C(K)\).
reviewed by: Hans Weber
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 815710
zbMATH Keywords: space of continuous functions
zbMATH Keywords: weak* convergence
zbMATH Keywords: compact quasi-Stonian space
zbMATH Keywords: sequentially order continuous linear functionals
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 815710