Statements (56)
| 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 |
| 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 |
gptkb:noncommutative_geometry
mathematical physics quantum mechanics |
| gptkbp:bfsParent |
gptkb:C*-algebra_K-theory
gptkb:Kasparov_KK-theory gptkb:operator_K-theory gptkb:K-theory gptkb:James_Glimm gptkb:Kaplansky_density_theorem |
| gptkbp:bfsLayer |
6
|
| https://www.w3.org/2000/01/rdf-schema#label |
C*-algebras
|