Noncommmutative Gelfand Duality for not necessarily unital $C^*$-algebras, Jordan Canonical form, and the existence of invariant subspaces

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dc.creatorPatel, Mukul S.
dc.date2005-08-27
dc.date.accessioned2026-07-07T05:22:44Z
dc.date.available2026-07-07T05:22:44Z
dc.descriptionGelfand-Naimark duality (Commutative $C^*$-algebras $\equiv$ Locally compact Hausdorff spaces) is extended to $C^*$-algebras $\equiv$ Quotient maps on locally compact Hausdorff spaces. Using this duality, we give for an \emph{arbitrary} bounded operator on a complex Hilbert space of several dimensions, a functional calculus and the existence theorem for nontrivial invariant subspace.
dc.descriptionUnder consideration for publication by Electronic Reasearch Announcements of the AMS
dc.identifierhttps://arxiv.org/abs/math/0508545
dc.identifierhttp://arxiv.org/abs/math/0508545
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76175
dc.subjectFunctional Analysis
dc.subjectOperator Algebras
dc.subject46L05; 47A13; 47A13; 43A40; 22B05
dc.titleNoncommmutative Gelfand Duality for not necessarily unital $C^*$-algebras, Jordan Canonical form, and the existence of invariant subspaces
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