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- Kaplansky_density_theorem abstract "In the theory of von Neumann algebras, the Kaplansky density theorem states that if A is a *-subalgebra of the algebra B(H) of bounded operators on a Hilbert space H, then the strong closure of the unit ball of A in B(H) is the unit ball of the strong closure of A in B(H). This gives a strengthening of the von Neumann bicommutant theorem, showing that an element a of the double commutant of A, denoted by A′′, can be strongly approximated by elements of A whose norm is no larger than that of a. The standard proof uses the fact that, when f is bounded, the continuous functional calculus a ↦ f(a) satisfies, for a net {aα} of self adjoint operatorsin the strong operator topology. This shows that self-adjoint part of the unit ball in A′′ can be approximated strongly by self-adjoint elements in the C*-algebra generated by A. A matrix computation then removes the self-adjointness restriction and proves the theorem.".
- Kaplansky_density_theorem wikiPageExternalLink VonNeumann2009.pdf.
- Kaplansky_density_theorem wikiPageID "9523634".
- Kaplansky_density_theorem wikiPageRevisionID "565895838".
- Kaplansky_density_theorem hasPhotoCollection Kaplansky_density_theorem.
- Kaplansky_density_theorem subject Category:Theorems_in_functional_analysis.
- Kaplansky_density_theorem subject Category:Von_Neumann_algebras.
- Kaplansky_density_theorem type Abstraction100002137.
- Kaplansky_density_theorem type Algebra106012726.
- Kaplansky_density_theorem type Cognition100023271.
- Kaplansky_density_theorem type Communication100033020.
- Kaplansky_density_theorem type Content105809192.
- Kaplansky_density_theorem type Discipline105996646.
- Kaplansky_density_theorem type KnowledgeDomain105999266.
- Kaplansky_density_theorem type Mathematics106000644.
- Kaplansky_density_theorem type Message106598915.
- Kaplansky_density_theorem type Proposition106750804.
- Kaplansky_density_theorem type PsychologicalFeature100023100.
- Kaplansky_density_theorem type PureMathematics106003682.
- Kaplansky_density_theorem type Science105999797.
- Kaplansky_density_theorem type Statement106722453.
- Kaplansky_density_theorem type Theorem106752293.
- Kaplansky_density_theorem type TheoremsInFunctionalAnalysis.
- Kaplansky_density_theorem type VonNeumannAlgebras.
- Kaplansky_density_theorem comment "In the theory of von Neumann algebras, the Kaplansky density theorem states that if A is a *-subalgebra of the algebra B(H) of bounded operators on a Hilbert space H, then the strong closure of the unit ball of A in B(H) is the unit ball of the strong closure of A in B(H). This gives a strengthening of the von Neumann bicommutant theorem, showing that an element a of the double commutant of A, denoted by A′′, can be strongly approximated by elements of A whose norm is no larger than that of a.".
- Kaplansky_density_theorem label "Dichtheitssatz von Kaplansky".
- Kaplansky_density_theorem label "Kaplansky density theorem".
- Kaplansky_density_theorem sameAs Dichtheitssatz_von_Kaplansky.
- Kaplansky_density_theorem sameAs m.02phs0_.
- Kaplansky_density_theorem sameAs Q1209546.
- Kaplansky_density_theorem sameAs Q1209546.
- Kaplansky_density_theorem sameAs Kaplansky_density_theorem.
- Kaplansky_density_theorem wasDerivedFrom Kaplansky_density_theorem?oldid=565895838.
- Kaplansky_density_theorem isPrimaryTopicOf Kaplansky_density_theorem.