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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 wikiPageLength "19263".
• Commutation_theorem wikiPageOutDegree "63".
• Commutation_theorem wikiPageRevisionID "705884982".
• Commutation_theorem wikiPageWikiLink Abelian_von_Neumann_algebra.
• Commutation_theorem wikiPageWikiLink Affiliated_operator.
• Commutation_theorem wikiPageWikiLink Bounded_operator.
• Commutation_theorem wikiPageWikiLink Category:Ergodic_theory.
• Commutation_theorem wikiPageWikiLink Category:Representation_theory_of_groups.
• Commutation_theorem wikiPageWikiLink Category:Theorems_in_functional_analysis.
• Commutation_theorem wikiPageWikiLink Category:Theorems_in_representation_theory.
• Commutation_theorem wikiPageWikiLink Category:Von_Neumann_algebras.
• Commutation_theorem wikiPageWikiLink Centralizer_and_normalizer.
• Commutation_theorem wikiPageWikiLink Countable_set.
• Commutation_theorem wikiPageWikiLink Crossed_product.
• Commutation_theorem wikiPageWikiLink Discrete_group.
• Commutation_theorem wikiPageWikiLink Dynamical_system.
• Commutation_theorem wikiPageWikiLink Equivalence_(measure_theory).
• Commutation_theorem wikiPageWikiLink Ergodic_theory.
• Commutation_theorem wikiPageWikiLink Finite_group.
• Commutation_theorem wikiPageWikiLink Francis_Joseph_Murray.
• Commutation_theorem wikiPageWikiLink Gelfand_pair.
• Commutation_theorem wikiPageWikiLink Haar_measure.
• Commutation_theorem wikiPageWikiLink Hilbert_space.
• Commutation_theorem wikiPageWikiLink Hilbert–Schmidt_operator.
• Commutation_theorem wikiPageWikiLink Inner_product_space.
• Commutation_theorem wikiPageWikiLink Irving_Segal.
• Commutation_theorem wikiPageWikiLink Jacques_Dixmier.
• Commutation_theorem wikiPageWikiLink John_von_Neumann.
• Commutation_theorem wikiPageWikiLink Local_quantum_field_theory.
• Commutation_theorem wikiPageWikiLink Locally_compact_group.
• Commutation_theorem wikiPageWikiLink Mathematics.
• Commutation_theorem wikiPageWikiLink Matrix_coefficient.
• Commutation_theorem wikiPageWikiLink Multiplication_operator.
• Commutation_theorem wikiPageWikiLink Plancherel_theorem.
• Commutation_theorem wikiPageWikiLink Plancherel_theorem_for_spherical_functions.
• Commutation_theorem wikiPageWikiLink Positive_element.
• Commutation_theorem wikiPageWikiLink Probability_measure.
• Commutation_theorem wikiPageWikiLink Probability_space.
• Commutation_theorem wikiPageWikiLink Quantum_statistical_mechanics.
• Commutation_theorem wikiPageWikiLink Regular_representation.
• Commutation_theorem wikiPageWikiLink Roger_Godement.
• Commutation_theorem wikiPageWikiLink Rudolf_Haag.
• Commutation_theorem wikiPageWikiLink State_(functional_analysis).
• Commutation_theorem wikiPageWikiLink Strong_operator_topology.
• Commutation_theorem wikiPageWikiLink Tensor_product.
• Commutation_theorem wikiPageWikiLink Tomita–Takesaki_theory.
• Commutation_theorem wikiPageWikiLink Trace_class.
• Commutation_theorem wikiPageWikiLink Unitary_operator.
• Commutation_theorem wikiPageWikiLink Unitary_representation.
• Commutation_theorem wikiPageWikiLink Von_Neumann_algebra.
• Commutation_theorem wikiPageWikiLinkText "Commutation theorem".
• Commutation_theorem wikiPageWikiLinkText "Commutation theorem#semilinearity".
• Commutation_theorem wikiPageWikiLinkText "von Neumann's commutation theorem".
• Commutation_theorem wikiPageUsesTemplate Template:Citation.
• Commutation_theorem wikiPageUsesTemplate Template:Harvtxt.
• Commutation_theorem wikiPageUsesTemplate Template:Reflist.
• Commutation_theorem wikiPageUsesTemplate Template:See_also.
• Commutation_theorem wikiPageUsesTemplate Template:Visible_anchor.
• 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 Algebra.
• Commutation_theorem type Process.
• Commutation_theorem type Redirect.
• Commutation_theorem type Theorem.
• Commutation_theorem type Thing.
• 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 seeAlso Tomita–Takesaki_theory.
• Commutation_theorem sameAs Q5155090.
• Commutation_theorem sameAs m.04f6ykv.
• Commutation_theorem sameAs Q5155090.
• Commutation_theorem wasDerivedFrom Commutation_theorem?oldid=705884982.
• Commutation_theorem isPrimaryTopicOf Commutation_theorem.