C*-algebras

GPTKB entity

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