The commutation theorem for tensor products over von Neumann algebras
type: Item
instance of: scholarly article
title: The commutation theorem for tensor products over von Neumann algebras
zbMATH Open document ID: 0951.46031
author: László Zsidó
author: Şerban Strătilă
published in: Journal of Functional Analysis
publication date: 2000-12-18T00:00:00Z
review text: Given a \(W^*\)-algebra \(M\), a \(W^*\)-algebra \(N\subset M\) containing \(1_M\) and two \(W^*\)-algebras \(M_1,M_2\subset N\), \(M\) is the tensor product over \(N\) of \(M_1\) and \(M_2\) if \(M= M_1\vee M_2\) and, in some spatial representation of \(M\), \(M_1\subset N\vee N_1\) and \(M_2\subset N\vee N_2\) for some commuting type \(I\) von Neumann subalgebras \(N_1,N_2\subset N\). The main result of this paper: \((M_1\vee M_2)'= (M_1'\cap N_1)\vee (M_2'\cap N_2)\vee (N\vee N_1\vee N_2)'\).
reviewed by: Bolis Basit
Mathematics Subject Classification ID: 46L06
Mathematics Subject Classification ID: 46L10
zbMATH DE Number: 1319964
zbMATH Keywords: \(W^*\)-algebra
zbMATH Keywords: tensor product
zbMATH Keywords: spatial representation
zbMATH Keywords: von Neumann subalgebras
MaRDI profile type: Publication
full work available at URL: jfan.1999.3408
OpenAlex ID: W1970547066
cites work: Q5626388
cites work: Convex analysis and measurable multifunctions
cites work: Une classification des facteurs de type ${\rm III}$
cites work: Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
cites work: The flow of weights on factors of type III
cites work: The numerical range and a certain convex set in an infinite factor
cites work: Interpolation by type I factors and the flip automorphism
cites work: Q3261641
cites work: Les anneaux d'opérateurs de classe finie
cites work: Q3994998
cites work: On tensor products of von Neumann algebras
cites work: Q3958960
cites work: Module Homomorphisms of a Von Neumann Algebra Into its Center
cites work: Irreducible Module Homomorphisms of a Von Neumann Algebra into its Center
cites work: Integral Decomposition of Functionals on C ∗ -Algebras
cites work: Essential central spectrum and range for elements of a von Neumann algebra
cites work: Strong continuity of operator functions
cites work: Modules Over Operator Algebras
cites work: On Homogeneous Measure Algebras
cites work: Inner Product Modules Over B ∗ -Algebras
cites work: Maximal injective subalgebras in factors associated with free groups
cites work: The Commutation Theorem for Tensor Products of von Neumann Algebras
cites work: Q5624220
cites work: On the Tensor Product of W * -Algebras
cites work: Q4002043
cites work: Q5631608
cites work: Positive Functions on C ∗ -Algebras
cites work: Q4741226
cites work: Q4143782
cites work: Q4172497
cites work: An algebraic reduction theory for W\(^*\)-algebras. I
cites work: Q5673440
cites work: On the direkt product of \(W^*\)-factors
cites work: Q3135819
cites work: Q5182153
DOI: 10.1006/JFAN.1999.3408
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description: scientific article; zbMATH DE number 1319964