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- Spectrum_of_a_C*-algebra abstract "In mathematics, the spectrum of a C*-algebra or dual of a C*-algebra A, denoted Â, is the set of unitary equivalence classes of irreducible *-representations of A. A *-representation π of A on a Hilbert space H is irreducible if, and only if, there is no closed subspace K different from H and {0} which is invariant under all operators π(x) with x ∈ A. We implicitly assume that irreducible representation means non-null irreducible representation, thus excluding trivial (i.e. identically 0) representations on one-dimensional spaces. As explained below, the spectrum  is also naturally a topological space; this is similar to the notion of the spectrum of a ring.One of the most important applications of this concept is to provide a notion of dual object for any locally compact group. This dual object is suitable for formulating a Fourier transform and a Plancherel theorem for unimodular separable locally compact groups of type I and a decomposition theorem for arbitrary representations of separable locally compact groups of type I. The resulting duality theory for locally compact groups is however much weaker than the Tannaka–Krein duality theory for compact topological groups or Pontryagin duality for locally compact abelian groups, both of which are complete invariants. That the dual is not a complete invariant is easily seen as the dual of any finite-dimensional full matrix algebra Mn(C) consists of a single point.".
- Spectrum_of_a_C*-algebra wikiPageID "918414".
- Spectrum_of_a_C*-algebra wikiPageLength "11808".
- Spectrum_of_a_C*-algebra wikiPageOutDegree "58".
- Spectrum_of_a_C*-algebra wikiPageRevisionID "700827592".
- Spectrum_of_a_C*-algebra wikiPageWikiLink Annihilator_(ring_theory).
- Spectrum_of_a_C*-algebra wikiPageWikiLink Banach_space.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Borel_set.
- Spectrum_of_a_C*-algebra wikiPageWikiLink C*-algebra.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Category:C*-algebras.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Category:Spectral_theory.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Compact_group.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Compact_space.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Connected_space.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Dimension.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Discrete_space.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Duality_(mathematics).
- Spectrum_of_a_C*-algebra wikiPageWikiLink Fourier_transform.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Gelfand_representation.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Gelfand–Naimark–Segal_construction.
- Spectrum_of_a_C*-algebra wikiPageWikiLink George_Mackey.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Group_algebra.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Haar_measure.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Hausdorff_space.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Heisenberg_group.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Hilbert_space.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Homeomorphism.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Idempotence.
- Spectrum_of_a_C*-algebra wikiPageWikiLink If_and_only_if.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Irreducible_representation.
- Spectrum_of_a_C*-algebra wikiPageWikiLink J._M._G._Fell.
- Spectrum_of_a_C*-algebra wikiPageWikiLink James_Glimm.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Kuratowski_closure_axioms.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Lie_group.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Locally_compact_group.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Locally_compact_space.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Natural_transformation.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Nilpotent.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Plancherel_theorem.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Polish_space.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Pontryagin_duality.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Primitive_ideal.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Quantum_state.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Ring_(mathematics).
- Spectrum_of_a_C*-algebra wikiPageWikiLink Semi-simplicity.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Separable_space.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Simple_module.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Space_(mathematics).
- Spectrum_of_a_C*-algebra wikiPageWikiLink Spectrum_of_a_ring.
- Spectrum_of_a_C*-algebra wikiPageWikiLink State_(functional_analysis).
- Spectrum_of_a_C*-algebra wikiPageWikiLink Surjective_function.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Tannaka–Krein_duality.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Topological_group.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Topological_space.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Topology.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Unitary_representation.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Weak_containment.
- Spectrum_of_a_C*-algebra wikiPageWikiLink Zariski_topology.
- Spectrum_of_a_C*-algebra wikiPageWikiLink File:3-dim_commut_algebra,_subalgebras,_ideals.svg.
- Spectrum_of_a_C*-algebra wikiPageWikiLinkText "Fell topology".
- Spectrum_of_a_C*-algebra wikiPageWikiLinkText "Spectrum of a C*-algebra".
- Spectrum_of_a_C*-algebra wikiPageWikiLinkText "dual object".
- Spectrum_of_a_C*-algebra wikiPageWikiLinkText "spectrum of a C*-algebra".
- Spectrum_of_a_C*-algebra wikiPageWikiLinkText "spectrum of the C*-algebra".
- Spectrum_of_a_C*-algebra wikiPageWikiLinkText "spectrum".
- Spectrum_of_a_C*-algebra wikiPageUsesTemplate Template:Functional_Analysis.
- Spectrum_of_a_C*-algebra subject Category:C*-algebras.
- Spectrum_of_a_C*-algebra subject Category:Spectral_theory.
- Spectrum_of_a_C*-algebra hypernym Set.
- Spectrum_of_a_C*-algebra type Algebra.
- Spectrum_of_a_C*-algebra comment "In mathematics, the spectrum of a C*-algebra or dual of a C*-algebra A, denoted Â, is the set of unitary equivalence classes of irreducible *-representations of A. A *-representation π of A on a Hilbert space H is irreducible if, and only if, there is no closed subspace K different from H and {0} which is invariant under all operators π(x) with x ∈ A. We implicitly assume that irreducible representation means non-null irreducible representation, thus excluding trivial (i.e.".
- Spectrum_of_a_C*-algebra label "Spectrum of a C*-algebra".
- Spectrum_of_a_C*-algebra sameAs Q7575320.
- Spectrum_of_a_C*-algebra sameAs m.03ptz5.
- Spectrum_of_a_C*-algebra sameAs Q7575320.
- Spectrum_of_a_C*-algebra wasDerivedFrom Spectrum_of_a_C*-algebra?oldid=700827592.
- Spectrum_of_a_C*-algebra isPrimaryTopicOf Spectrum_of_a_C*-algebra.