Statements (58)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:alsoKnownAs |
gptkb:W*-algebras
|
| gptkbp:application |
mathematical physics
noncommutative geometry quantum mechanics |
| gptkbp:class |
gptkb:type_I
type II type III |
| gptkbp:contains |
self-adjoint operators
unitary operators projections |
| gptkbp:definedIn |
*-algebras of bounded operators on a Hilbert space closed in the weak operator topology and containing the identity operator
|
| gptkbp:field |
functional analysis
operator algebras |
| gptkbp:hasConcept |
factor
trace modular theory center of a von Neumann algebra |
| gptkbp:hasSubfield |
factors
Cartan subalgebras abelian von Neumann algebras finite von Neumann algebras hyperfinite II_1 factor infinite von Neumann algebras injective von Neumann algebras masa (maximal abelian self-adjoint subalgebra) type III factors type II_1 factors |
| https://www.w3.org/2000/01/rdf-schema#label |
von Neumann algebras
|
| gptkbp:importantFor |
gptkb:double_commutant_theorem
|
| gptkbp:importantMathematician |
gptkb:John_von_Neumann
gptkb:Francis_J._Murray |
| gptkbp:introducedIn |
1930s
|
| gptkbp:namedAfter |
gptkb:John_von_Neumann
|
| gptkbp:property |
closed under adjoint operation
closed in weak operator topology contains identity operator |
| gptkbp:relatedTo |
gptkb:C*-algebras
gptkb:Tomita–Takesaki_theory crossed product direct integral decomposition group von Neumann algebras hyperfinite factors subfactors |
| gptkbp:usedIn |
gptkb:logic
gptkb:quantum_field_theory gptkb:statistical_mechanics ergodic theory representation theory noncommutative probability |
| gptkbp:bfsParent |
gptkb:C*-algebras
gptkb:K-theory_of_operator_algebras gptkb:Operator_algebras gptkb:Haagerup_property gptkb:Kaplansky_density_theorem gptkb:Noncommutative_Geometry gptkb:GNS_construction |
| gptkbp:bfsLayer |
6
|