Statements (53)
Predicate | Object |
---|---|
gptkbp:instanceOf |
gptkb:algebra
|
gptkbp:C*-identity |
||a*a|| = ||a||^2
|
gptkbp:definedIn |
Banach algebra with involution satisfying the C*-identity
|
gptkbp:example |
algebra of bounded operators on a Hilbert space
algebra of continuous functions on a compact space |
gptkbp:field |
gptkb:mathematics
functional analysis operator algebras |
gptkbp:generalizes |
algebra of bounded operators on a Hilbert space
|
gptkbp:hasApplication |
gptkb:quantum_field_theory
gptkb:statistical_mechanics dynamical systems representation theory |
gptkbp:hasProperty |
gptkb:associative_algebra
ideals irreducible representations tensor products closed under adjoint operation commutative C*-algebras crossed products involutive algebra non-unital C*-algebras noncommutative C*-algebras norm-closed positive elements pure states quotients self-adjoint elements form a real vector space simple C*-algebras states (positive linear functionals of norm 1) unital C*-algebras unitary elements |
https://www.w3.org/2000/01/rdf-schema#label |
C*-algebras
|
gptkbp:introduced |
gptkb:John_von_Neumann
gptkb:Francis_J._Murray |
gptkbp:introducedIn |
1940s
|
gptkbp:namedAfter |
C (complex numbers)
|
gptkbp:relatedTo |
gptkb:K-theory
gptkb:Gelfand_representation gptkb:von_Neumann_algebras spectral theory noncommutative topology |
gptkbp:studiedBy |
gptkb:Gelfand–Naimark_theorem
|
gptkbp:subcategory_of |
gptkb:Banach_algebras
operator algebras topological algebras |
gptkbp:used_in |
mathematical physics
noncommutative geometry quantum mechanics |
gptkbp:bfsParent |
gptkb:K-theory
gptkb:C*-algebra gptkb:Gelfand–Naimark–Segal_construction |
gptkbp:bfsLayer |
5
|