Noncommmutative theorems: Gelfand Duality, Spectral, Invariant Subspace, and Pontryagin Duality

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dc.creatorPatel, Mukul S.
dc.date2005-03-07
dc.date.accessioned2026-07-07T05:17:45Z
dc.date.available2026-07-07T05:17:45Z
dc.descriptionWe extend the Gelfand-Naimark duality of commutative C*-algebras, "A COMMUTATIVE C*-ALGEBRA -- A LOCALLY COMPACT HAUSDORFF SPACE" to "A C*-ALGEBRA--A QUOTIENT OF A LOCALLY COMPACT HAUSDORFF SPACE". Thus, a C*-algebra is isomorphic to the convolution algebra of continuous regular Borel measures on the topological equivalence relation given by the above mentioned quotient. In commutative case this reduces to Gelfand-Naimark theorem. Applications: 1) A simultaneous extension, to arbitrary Hilbert space operators, of Jordan Canonical Form and Spectral Theorem of normal operators 2) A functional calculus for arbitrary operators. 3) Affirmative solution of Invariant Subspace Problem. 4) Extension of Pontryagin duality to nonabelian groups, and inevitably to groups whose underlying topological space is noncommutative.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0503127
dc.identifierhttp://arxiv.org/abs/math/0503127
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74420
dc.subjectOperator Algebras
dc.subjectQuantum Algebra
dc.subject46L05; 47A65; 47A13; 22B05
dc.titleNoncommmutative theorems: Gelfand Duality, Spectral, Invariant Subspace, and Pontryagin Duality
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