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- Von_Neumann_bicommutant_theorem abstract "In mathematics, specifically functional analysis, the von Neumann bicommutant theorem relates the closure of a set of bounded operators on a Hilbert space in certain topologies to the bicommutant of that set. In essence, it is a connection between the algebraic and topological sides of operator theory.The formal statement of the theorem is as follows: Von Neumann Bicommutant Theorem. Let M be an algebra of bounded operators on a Hilbert space H, containing the identity operator and closed under taking adjoints. Then the closures of M in the weak operator topology and the strong operator topology are equal, and are in turn equal to the bicommutant M′′ of M. This algebra is the von Neumann algebra generated by M.There are several other topologies on the space of bounded operators, and one can ask what are the *-algebras closed in these topologies. If M is closed in the norm topology then it is a C*-algebra, but not necessarily a von Neumann algebra. One such example is the C*-algebra of compact operators (on an infinite dimensional Hilbert space). For most other common topologies the closed *-algebras containing 1 are still von Neumann algebras; this applies in particular to the weak operator, strong operator, *-strong operator, ultraweak, ultrastrong, and *-ultrastrong topologies.It is related to the Jacobson density theorem.".
- Von_Neumann_bicommutant_theorem wikiPageID "455962".
- Von_Neumann_bicommutant_theorem wikiPageLength "8072".
- Von_Neumann_bicommutant_theorem wikiPageOutDegree "41".
- Von_Neumann_bicommutant_theorem wikiPageRevisionID "681321384".
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Algebra.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Approximate_identity.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Bicommutant.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Bounded_operator.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink C*-algebra.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Category:Articles_containing_proofs.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Category:Operator_theory.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Category:Theorems_in_functional_analysis.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Category:Von_Neumann_algebras.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Centralizer_and_normalizer.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Closed_set.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Closure_(mathematics).
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Closure_(topology).
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Compact_operator_on_Hilbert_space.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Complete_metric_space.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Functional_analysis.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Hermitian_adjoint.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Hilbert_space.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Jacobson_density_theorem.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Mathematics.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Operator_algebra.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Operator_norm.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Operator_theory.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Operator_topologies.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Projection_(linear_algebra).
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Strong_operator_topology.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Subalgebra.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Ultrastrong_topology.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Ultraweak_topology.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Vector_space.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Von_Neumann_algebra.
- Von_Neumann_bicommutant_theorem wikiPageWikiLink Weak_operator_topology.
- Von_Neumann_bicommutant_theorem wikiPageWikiLinkText "Von Neumann bicommutant theorem".
- Von_Neumann_bicommutant_theorem wikiPageWikiLinkText "von Neumann bicommutant theorem".
- Von_Neumann_bicommutant_theorem date "September 2015".
- Von_Neumann_bicommutant_theorem reason "If M acts non-degenerately, it can be identified bijectively with its image A in L. Is the image being a sub-C*-algebra an additional hypothesis on the representation, or is it automatic at this point? The only obstacle I can see is being weakly closed, but maybe this is automatic.".
- Von_Neumann_bicommutant_theorem reason "This part is incomplete since we must intersect a finite number of these subbasic open sets.".
- Von_Neumann_bicommutant_theorem reason "What kind of algebra?".
- Von_Neumann_bicommutant_theorem wikiPageUsesTemplate Template:!!.
- Von_Neumann_bicommutant_theorem wikiPageUsesTemplate Template:=.
- Von_Neumann_bicommutant_theorem wikiPageUsesTemplate Template:Clarify.
- Von_Neumann_bicommutant_theorem wikiPageUsesTemplate Template:Math.
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- Von_Neumann_bicommutant_theorem wikiPageUsesTemplate Template:What.
- Von_Neumann_bicommutant_theorem subject Category:Articles_containing_proofs.
- Von_Neumann_bicommutant_theorem subject Category:Operator_theory.
- Von_Neumann_bicommutant_theorem subject Category:Theorems_in_functional_analysis.
- Von_Neumann_bicommutant_theorem subject Category:Von_Neumann_algebras.
- Von_Neumann_bicommutant_theorem type Algebra.
- Von_Neumann_bicommutant_theorem type Physic.
- Von_Neumann_bicommutant_theorem type Proof.
- Von_Neumann_bicommutant_theorem type Theorem.
- Von_Neumann_bicommutant_theorem comment "In mathematics, specifically functional analysis, the von Neumann bicommutant theorem relates the closure of a set of bounded operators on a Hilbert space in certain topologies to the bicommutant of that set. In essence, it is a connection between the algebraic and topological sides of operator theory.The formal statement of the theorem is as follows: Von Neumann Bicommutant Theorem.".
- Von_Neumann_bicommutant_theorem label "Von Neumann bicommutant theorem".
- Von_Neumann_bicommutant_theorem sameAs Q528987.
- Von_Neumann_bicommutant_theorem sameAs Théorème_du_bicommutant_de_von_Neumann.
- Von_Neumann_bicommutant_theorem sameAs m.02bnn5.
- Von_Neumann_bicommutant_theorem sameAs Q528987.
- Von_Neumann_bicommutant_theorem wasDerivedFrom Von_Neumann_bicommutant_theorem?oldid=681321384.
- Von_Neumann_bicommutant_theorem isPrimaryTopicOf Von_Neumann_bicommutant_theorem.