Conjugacy of involutive antiautomorphisms of von Neumann algebras
type: Item
instance of: scholarly article
title: Conjugacy of involutive antiautomorphisms of von Neumann algebras
zbMATH Open document ID: 0615.46055
DOI: 10.1016/0022-1236(86)90080-7
author: Erling Størmer
published in: Journal of Functional Analysis
publication date: 1986-01-01T00:00:00Z
review text: A central involution of a von Neumann algebra is a *-antiautomorphism of order 2 leaving the center elementwise fixed. It is proved that two central involutions of a von Neumann algebra are conjugate via a *- automorphism leaving the center elementwise fixed if and only if the corresponding Jordan algebras of selfadjoint fixed points are isomorphic via an isomorphism leaving the center elementwise fixed. Since there are von Neumann algebras with many conjugacy classes of central involutions and the Jordan algebra of selfadjoint fixed points usually generates the von Neumann algebra it is thus shown that there may be even an uncountable number of non-isomorphic JW-algebras generating the same von Neumann algebra. The paper also discusses the problem if two close central involutions are conjugate.
reviewed by: Tage Bai Andersen
Mathematics Subject Classification ID: 46L10
Mathematics Subject Classification ID: 46L70
zbMATH DE Number: 3996419
zbMATH Keywords: central involution of a von Neumann algebra
zbMATH Keywords: conjugacy classes of central involutions
zbMATH Keywords: Jordan algebra of selfadjoint fixed points
zbMATH Keywords: JW-algebras
MaRDI profile type: Publication
full work available at URL: 0022-1236(86)90080-7
OpenAlex ID: W2055784606
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description: scientific article; zbMATH DE number 3996419