Variations on a theme of Gelfand and Naimark

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dc.creatorCarrion-Alvarez, Miguel
dc.date2004-02-10
dc.date.accessioned2026-07-07T05:05:18Z
dc.date.available2026-07-07T05:05:18Z
dc.descriptionC*-algebras are widely used in mathematical physics to represent the observables of physical systems, and are sometimes taken as the starting point for rigorous formulations of quantum mechanics and classical statistical mechanics. Nevertheless, in many cases the naive choice of an algebra of observables does not admit a C*-algebra structure, and some massaging is necessary. In this paper we investigate what properties of C*-algebras carry over to more general algebras and what modifications of the Gelfand theory of normed algebras are necessary. We use category theory as a guide and, by replacing the ordinary definition of the Gelfand spectrum with a manifestly functorial definition, we succeed in generalizing the Gelfand-Naimark theorem to locally convex *-algebras. We also recall a little-known but potentially very useful generalization of the Stone-Weierstrass theorem to completely regular, Hausdorff spaces.
dc.descriptionLaTeX, 19 pages, no figures, uses packages xypic and amssymb
dc.identifierhttps://arxiv.org/abs/math/0402150
dc.identifierhttp://arxiv.org/abs/math/0402150
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70114
dc.subjectFunctional Analysis
dc.subjectMathematical Physics
dc.subjectCategory Theory
dc.subject46M99 (primary) 47L90 (secondary)
dc.titleVariations on a theme of Gelfand and Naimark
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