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Commutation properties of automorphism groups and mappings of von Neumann algebras
Journal article   Open access   Peer reviewed

Commutation properties of automorphism groups and mappings of von Neumann algebras

Journal of functional analysis, Vol.34(1), pp.138-145
1979
DOI: 10.1016/0022-1236(79)90029-6
url
https://doi.org/10.1016/0022-1236(79)90029-6View
Published (Version of record) Open Access

Abstract

We prove a commutation theorem for point ultraweakly continuous oneparameter groups of automorphisms of von Neumann algebras. If α t , is such a group in Aut( R ) for a von Neumann algebra R , we show the equivalence of the following three conditions on an ultraweakly continuous linear transformation μ: R → R : (a) μ commutes weakly with the infinitesimal generator for α t ; (b) μ ° α t = α t ° μ , t ∈ R ; and ( c ) μ leaves invariant each of the spectral subspaces associated with α t . A simple condition which is applicable when μ is an automorphism is pointed out.

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