Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
An algebra of operators on a Hilbert space is reflexive if it coincides with the algebra of all operators leaving invariant every subspace invariant under the algebra.
|
| gptkbp:example |
Algebra of all bounded operators on a Hilbert space
Von Neumann algebra |
| gptkbp:field |
gptkb:Operator_algebras
Functional analysis |
| gptkbp:hasSubgroup |
gptkb:Operator_algebras
|
| https://www.w3.org/2000/01/rdf-schema#label |
Reflexive Algebras
|
| gptkbp:introduced |
gptkb:Paul_Halmos
|
| gptkbp:introducedIn |
1950s
|
| gptkbp:property |
Every von Neumann algebra is reflexive
Not every reflexive algebra is a von Neumann algebra |
| gptkbp:relatedTo |
Algebra of operators
Invariant subspace |
| gptkbp:seeAlso |
gptkb:Double_commutant_theorem
Commutant |
| gptkbp:bfsParent |
gptkb:Nest_Algebras
|
| gptkbp:bfsLayer |
7
|