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- Q5155090 subject Q10129880.
- Q5155090 subject Q7452174.
- Q5155090 subject Q8653265.
- Q5155090 subject Q8851992.
- Q5155090 subject Q8907073.
- Q5155090 abstract "In mathematics, a commutation theorem explicitly identifies the commutant of a specific von Neumann algebra acting on a Hilbert space in the presence of a trace. The first such result was proved by F.J. Murray and John von Neumann in the 1930s and applies to the von Neumann algebra generated by a discrete group or by the dynamical system associated with ameasurable transformation preserving a probability measure. Another important application is in the theory of unitary representations of unimodular locally compact groups, where the theory has been applied to the regular representation and other closely related representations. In particular this framework led to an abstract version of the Plancherel theorem for unimodular locally compact groups due to Irving Segal and Forrest Stinespring and an abstract Plancherel theorem for spherical functions associated with a Gelfand pair due to Roger Godement. Their work was put in final form in the 1950s by Jacques Dixmier as part of the theory of Hilbert algebras. It was not until the late 1960s, prompted partly by results in algebraic quantum field theory and quantum statistical mechanics due to the school of Rudolf Haag, that the more general non-tracial Tomita–Takesaki theory was developed, heralding a new era in the theory of von Neumann algebras.".
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- Q5155090 wikiPageWikiLink Q7452174.
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- Q5155090 wikiPageWikiLink Q8653265.
- Q5155090 wikiPageWikiLink Q8851992.
- Q5155090 wikiPageWikiLink Q8907073.
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- Q5155090 type Thing.
- Q5155090 comment "In mathematics, a commutation theorem explicitly identifies the commutant of a specific von Neumann algebra acting on a Hilbert space in the presence of a trace. The first such result was proved by F.J. Murray and John von Neumann in the 1930s and applies to the von Neumann algebra generated by a discrete group or by the dynamical system associated with ameasurable transformation preserving a probability measure.".
- Q5155090 label "Commutation theorem".
- Q5155090 seeAlso Q7818977.