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See Also: group  -algebra, von Neumann algebra, noncommutative geometry, groupoid C*-convolution algebras, groupoid C*-dynamical system, compact quantum groupoids related to C*-algebras, nuclear C*-algebra, -algebra homomorphisms are continuous, continuous linear mapping, operator norm, uniform continuity over locally compact quantum groupoids, -algebra, norm and spectral radius in -algebras, equivalence of definitions of -algebra, decomposition of self-adjoint elements in positive and negative parts, Gelfand-Naimark-Segal construction, Gelfand transform
| Other names: |
C*-algebra, C* algebra |
| Also defines: |
 axiom |
| Keywords: |
C*-algebra properties, relation to groupoids, norm and spectral radius, noncommutative C*-algebras, C*-axiom |
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Cross-references: von Neumann algebras, essential supremum, pointwise operations, measure space, ideal, compact operators, open, closed, Gelfand-Naimark representation theorem, information, link, Noncommutative Topology, projections, connected, unitization, compactification, topological space, properties, Gelfand-Naimark theorem, commutative, functional analysis, theorem, operator norm, adjoint, bounded operators, inner product, vanish at infinity, locally compact Hausdorff space, locally compact, limit, uniform convergence, pointwise, operation, Hausdorff topological space, compact, class, terms, positive linear functionals, sequences, monotonic, monotonic functions, partial ordering, theory, negative, self-adjoint element, imaginary parts, complex, decompositions, numbers, real numbers, multiplication, addition, closed under, unit circle, real functions, frame, complex conjugation, functions, complex analysis, interpretations, useful, definitions, involutory rings, semi-simple, continuous, *-homomorphisms, normed algebras, implies, even, identity element, element, spectral radius, consequence, topological algebras, equality, involution, norm, algebras, defining property, noncommutative, knots, locally compact topological spaces, Lie group representations, Hilbert spaces, operators, Banach algebras, involutive
There are 43 references to this entry.
This is version 31 of -algebra, born on 2002-08-23, modified 2009-01-29.
Object id is 3334, canonical name is CAlgebra.
Accessed 7089 times total.
Classification:
| AMS MSC: | 46L05 (Functional analysis :: Selfadjoint operator algebras :: General theory of $C^*$-algebras) | | | 46L87 (Functional analysis :: Selfadjoint operator algebras :: Noncommutative differential geometry) |
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Pending Errata and Addenda
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