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- Commutation_theorem 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.".
- Commutation_theorem wikiPageID "18404411".
- Commutation_theorem wikiPageRevisionID "598729022".
- Commutation_theorem hasPhotoCollection Commutation_theorem.
- Commutation_theorem subject Category:Ergodic_theory.
- Commutation_theorem subject Category:Representation_theory_of_groups.
- Commutation_theorem subject Category:Theorems_in_functional_analysis.
- Commutation_theorem subject Category:Theorems_in_representation_theory.
- Commutation_theorem subject Category:Von_Neumann_algebras.
- Commutation_theorem type Abstraction100002137.
- Commutation_theorem type Algebra106012726.
- Commutation_theorem type Cognition100023271.
- Commutation_theorem type Communication100033020.
- Commutation_theorem type Content105809192.
- Commutation_theorem type Discipline105996646.
- Commutation_theorem type KnowledgeDomain105999266.
- Commutation_theorem type Mathematics106000644.
- Commutation_theorem type Message106598915.
- Commutation_theorem type Proposition106750804.
- Commutation_theorem type PsychologicalFeature100023100.
- Commutation_theorem type PureMathematics106003682.
- Commutation_theorem type Science105999797.
- Commutation_theorem type Statement106722453.
- Commutation_theorem type Theorem106752293.
- Commutation_theorem type TheoremsInFunctionalAnalysis.
- Commutation_theorem type TheoremsInRepresentationTheory.
- Commutation_theorem type VonNeumannAlgebras.
- Commutation_theorem 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.".
- Commutation_theorem label "Commutation theorem".
- Commutation_theorem sameAs m.04f6ykv.
- Commutation_theorem sameAs Q5155090.
- Commutation_theorem sameAs Q5155090.
- Commutation_theorem sameAs Commutation_theorem.
- Commutation_theorem wasDerivedFrom Commutation_theorem?oldid=598729022.
- Commutation_theorem isPrimaryTopicOf Commutation_theorem.