The commutant modulo the set of compact operators of a von Neumann algebra
type: Item
instance of: scholarly article
title: The commutant modulo the set of compact operators of a von Neumann algebra
zbMATH Open document ID: 0632.46053
DOI: 10.1016/0022-1236(87)90011-5
author: Sorin Popa
published in: Journal of Functional Analysis
publication date: 1987-01-01T00:00:00Z
review text: Let B(H) be the algebra of bounded operators on a Hilbert space H and let K(H)\(\subset B(H)\) be the ideal of compact operators on H. One of the interesting results the author proves is: Let M be a von Neumann algebra acting on the Hilbert space H. If T is an operator on H such that Tx-xT\(\in K(H)\) for all \(x\in M\) then there exists \(T\in M'\) such that T-T'\(\in K(H)\). Here T' and M' are the commutants of T and M, respectively.
Mathematics Subject Classification ID: 46L10
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 4028171
zbMATH Keywords: commutant modulo the set of compact operators of a von Neumann algebra
zbMATH Keywords: \(pre\)-C\({}^ *\)-algebra
reviewed by: B. D. Malviya
MaRDI profile type: Publication
full work available at URL: 0022-1236(87)90011-5
OpenAlex ID: W1978240114
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description: scientific article; zbMATH DE number 4028171