Every \(L_ 1\)-predual is complemented in a simplex space
type: Item
instance of: scholarly article
title: Every \(L_ 1\)-predual is complemented in a simplex space
zbMATH Open document ID: 0691.46005
DOI: 10.1007/BF02787221
author: Wolfgang Lusky
published in: Israel Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Assume that all Banach spaces are real. By a simplex S one means a compact Choquet simplex; the corresponding simplex space is defined to be \(A(S)=\{f: S\to R:\) f affine and continuous\} \textit{A. J. Lazar} and \textit{J. Lindenstrauss} [Acta Math. 126, 165-194 (1971; Zbl 0209.432)] proved that for any separable \(L_ 1\)-predual space X there is a separable simplex space A(S)\(\supset X\) and contractive projection \(P: A(S)\to X.\) Lazar and Lindenstrauss posed the problem whether the above result remains true without the assumption of separability. In this interesting paper the author supplies positive answer to this question.
Mathematics Subject Classification ID: 46B10
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 4131009
zbMATH Keywords: isometric involutive map
zbMATH Keywords: complemented spaces
zbMATH Keywords: compact Choquet simplex
zbMATH Keywords: simplex space
zbMATH Keywords: separable \(L_ 1\)-predual
zbMATH Keywords: contractive projection
MaRDI profile type: Publication
cites work: Q3900495
cites work: On a class of real Banach spaces
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cites work: Q4107071
cites work: Banach spaces whose duals are \(L_ 1\) spaces and their representing matrices
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description: scientific article; zbMATH DE number 4131009