Journal article
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
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.
Details
- Title: Subtitle
- Commutation properties of automorphism groups and mappings of von Neumann algebras
- Creators
- Palle E.T Jorgensen
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.34(1), pp.138-145
- DOI
- 10.1016/0022-1236(79)90029-6
- ISSN
- 1096-0783
- eISSN
- 1096-0783
- Language
- English
- Date published
- 1979
- Academic Unit
- Mathematics
- Record Identifier
- 9983985973202771
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