Noncommutative Gelfand Duality and Applications I: The Existence of invariant subspaces

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dc.creatorPatel, Mukul S.
dc.date2008-11-12
dc.date.accessioned2026-07-07T10:17:40Z
dc.date.available2026-07-07T10:17:40Z
dc.descriptionGelfand duality between unital commutative C*-algebras and Compact Hausdorff spaces is extended to all unital C*-algebras, where the dual objects are what we call compact Hausdorff quantum spaces. We apply this result to obtain, a characterization of unitary groups of C*-algebras, and, for arbitrary bounded Hilbert space operators, (i) A spectral theorem cum continuous functional calculus, and (ii) A proof of the general Invariant Subspace Theorem. Also described is a nonabelian generalization of Pontryagin duality of abelian locally compact groups.
dc.identifierhttps://arxiv.org/abs/0811.1824
dc.identifierhttp://arxiv.org/abs/0811.1824
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173930
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.subject46L05; 46L85; 47A15
dc.titleNoncommutative Gelfand Duality and Applications I: The Existence of invariant subspaces
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