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- Abelian_von_Neumann_algebra abstract "In functional analysis, an abelian von Neumann algebra is a von Neumann algebra of operators on a Hilbert space in which all elements commute. The prototypical example of an abelian von Neumann algebra is the algebra L∞(X, μ) for μ a σ-finite measure on X realized as an algebra of operators on the Hilbert space L2(X, μ) as follows: Each f ∈ L∞(X, μ) is identified with the multiplication operatorOf particular importance are the abelian von Neumann algebras on separable Hilbert spaces, particularly since they are completely classifiable by simple invariants.Though there is a theory for von Neumann algebras on non-separable Hilbert spaces (and indeed much of the general theory still holds in that case) the theory is considerably simpler for algebras on separable spaces and most applications to other areas of mathematics or physics only use separable Hilbert spaces. Note that if the measure spaces (X, μ) is a standard measure space (that is X − N is a standard Borel space for some null set N and μ is a σ-finite measure) then L2(X, μ) is separable.".
- Abelian_von_Neumann_algebra wikiPageID "1496379".
- Abelian_von_Neumann_algebra wikiPageRevisionID "543947349".
- Abelian_von_Neumann_algebra hasPhotoCollection Abelian_von_Neumann_algebra.
- Abelian_von_Neumann_algebra subject Category:Von_Neumann_algebras.
- Abelian_von_Neumann_algebra type Abstraction100002137.
- Abelian_von_Neumann_algebra type Algebra106012726.
- Abelian_von_Neumann_algebra type Cognition100023271.
- Abelian_von_Neumann_algebra type Content105809192.
- Abelian_von_Neumann_algebra type Discipline105996646.
- Abelian_von_Neumann_algebra type KnowledgeDomain105999266.
- Abelian_von_Neumann_algebra type Mathematics106000644.
- Abelian_von_Neumann_algebra type PsychologicalFeature100023100.
- Abelian_von_Neumann_algebra type PureMathematics106003682.
- Abelian_von_Neumann_algebra type Science105999797.
- Abelian_von_Neumann_algebra type VonNeumannAlgebras.
- Abelian_von_Neumann_algebra comment "In functional analysis, an abelian von Neumann algebra is a von Neumann algebra of operators on a Hilbert space in which all elements commute.".
- Abelian_von_Neumann_algebra label "Abelian von Neumann algebra".
- Abelian_von_Neumann_algebra label "Abelsche von-Neumann-Algebra".
- Abelian_von_Neumann_algebra label "Álgebra abeliana de von Neumann".
- Abelian_von_Neumann_algebra sameAs Abelsche_von-Neumann-Algebra.
- Abelian_von_Neumann_algebra sameAs Álgebra_abeliana_de_von_Neumann.
- Abelian_von_Neumann_algebra sameAs m.055y7z.
- Abelian_von_Neumann_algebra sameAs Q4666687.
- Abelian_von_Neumann_algebra sameAs Q4666687.
- Abelian_von_Neumann_algebra sameAs Abelian_von_Neumann_algebra.
- Abelian_von_Neumann_algebra wasDerivedFrom Abelian_von_Neumann_algebra?oldid=543947349.
- Abelian_von_Neumann_algebra isPrimaryTopicOf Abelian_von_Neumann_algebra.