Images of contractive projections on operator algebras
type: Item
instance of: scholarly article
title: Images of contractive projections on operator algebras
zbMATH Open document ID: 1019.46037
DOI: 10.1016/S0022-247X(02)00132-4
author: Antonio M. Peralta
author: Leslie J. Bunce
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-11-28T00:00:00Z
review text: JW*-triples, that is, weak*-closed subspaces of \(B(H)\) that are also closed under \(x \to xx^{\ast}x\), arise as images of contractive (i.e., norm one) projections on von Neumann algebras. Their generalisations, JBW*-triples, are those complex Banach dual spaces whose open unit balls are bounded symmetric domains. In this paper, the authors investigate the contractive projections on a JBW*-triple. They show that if \(P\) is a weak*-continuous contractive projection on a JBW*-triple \(M\), then \(P(M)\) is of type I or semifinite, respectively, if \(M\) is of the corresponding type. They also show that \(P(M)\) has no infinite spin part if \(M\) is a type I von Neumann algebra.
Mathematics Subject Classification ID: 46L70
zbMATH DE Number: 1836777
zbMATH Keywords: JBW*-triples
zbMATH Keywords: contractive projections
reviewed by: Jianlian Cui
MaRDI profile type: Publication
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full work available at URL: s0022-247x(02)00132-4
OpenAlex ID: W2162898899
description: scientific article; zbMATH DE number 1836777