Analytic crossed products and outer conjugacy classes of automorphisms of von Neumann algebras. II
type: Item
instance of: scholarly article
title: Analytic crossed products and outer conjugacy classes of automorphisms of von Neumann algebras. II
zbMATH Open document ID: 0613.46055
DOI: 10.1007/BF01456189
author: Paul S. Muhly
author: Kiche-Suke Saito
published in: Mathematische Annalen
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164305
review text: Let M be a von Neumann algebra and let \(\alpha\) be a *-automorphism of M. The analytic crossed product of M with \(\alpha\), \(M\times _{\alpha}{\mathbb{Z}}_ +\), is constructed from M and the non-negative powers of \(\alpha\) in much the same way as the von Neumann algebra crossed product of M with \(\alpha\) is constructed from M and the entire group \(\{\alpha ^ n\}_{n\in {\mathbb{Z}}}\). \(M\times _{\alpha}{\mathbb{Z}}_ +\) should be viewed as a noncommutative version of \(H^{\infty}({\mathbb{T}}).\) In this note we show that under suitable hypotheses, if two analytic crossed products are isomorphic then the associated automorphisms are outer conjugate. Our results generalize results by Arveson and by Arveson and Josephson who considered the case when the coefficient algebra M is abelian. This note also generalizes our earlier study on the same subject. The hypotheses in that work are weakened considerably while new and simpler proofs are given.
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L40
zbMATH DE Number: 3992199
zbMATH Keywords: outer conjugacy classes of automorphisms
zbMATH Keywords: *-automorphism
zbMATH Keywords: analytic crossed product
zbMATH Keywords: von Neumann algebra crossed product
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3992199