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gptkbp:instanceOf
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Mathematical structure
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gptkbp:alsoKnownAs
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gptkb:W*-algebras
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gptkbp:application
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gptkb:quantum_field_theory
gptkb:Quantum_mechanics
Noncommutative geometry
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gptkbp:characterizedBy
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gptkb:Double_commutant_theorem
Predual existence
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gptkbp:definedIn
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*-algebras of bounded operators on a Hilbert space closed in the weak operator topology and containing the identity operator
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gptkbp:field
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gptkb:Operator_algebras
Functional analysis
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gptkbp:hasConcept
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gptkb:Modular_theory
Center
Factor
Trace
Projection
Commutant
Predual
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gptkbp:hasInvariant
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gptkb:Modular_automorphism_group
Center
Trace
Dimension function
Type classification
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gptkbp:hasProperty
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Closed in weak operator topology
Closed under adjoint
Contains identity operator
Double commutant equals itself
Has predual
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gptkbp:hasType
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Type I
Type II
Type III
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https://www.w3.org/2000/01/rdf-schema#label
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Von Neumann Algebras
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gptkbp:introducedIn
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1930s
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gptkbp:namedAfter
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gptkb:John_von_Neumann
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gptkbp:relatedTo
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gptkb:C*-algebras
gptkb:Hilbert_space
gptkb:Noncommutative_probability
gptkb:Quantum_probability
Functional analysis
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gptkbp:studiedBy
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gptkb:John_von_Neumann
gptkb:Francis_J._Murray
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gptkbp:subclassOf
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gptkb:C*-algebra
gptkb:Operator_algebra
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gptkbp:subunit
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Center
Factor
Commutant
Predual
Projection lattice
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gptkbp:bfsParent
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gptkb:Jacques_Dixmier
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gptkbp:bfsLayer
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6
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