On quantales and spectra of C*-algebras

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dc.creatorKruml, David
dc.creatorPelletier, Joan Wick
dc.creatorResende, Pedro
dc.creatorRosicky, Jiri
dc.date2002-11-21
dc.date.accessioned2026-07-07T04:53:10Z
dc.date.available2026-07-07T04:53:10Z
dc.descriptionWe study properties of the quantale spectrum Max A of an arbitrary unital C*-algebra A. In particular we show that the spatialization of Max A with respect to one of the notions of spatiality in the literature yields the locale of closed ideals of A when A is commutative. We study under general conditions functors with this property, in addition requiring that colimits be preserved, and we conclude in this case that the spectrum of A necessarily coincides with the locale of closed ideals of the commutative reflection of A. Finally, we address functorial properties of Max, namely studying (non-)preservation of limits and colimits. Although Max is not an equivalence of categories, therefore not providing a direct generalization of Gelfand duality to the noncommutative case, it is a faithful complete invariant of unital C*-algebras.
dc.description22 pages. Will appear in Applied Categorical Structures
dc.identifierhttps://arxiv.org/abs/math/0211345
dc.identifierhttp://arxiv.org/abs/math/0211345
dc.identifierApplied Categorical Structures 11 (2003) 543-560
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65746
dc.subjectOperator Algebras
dc.subjectCategory Theory
dc.subject46L85 (Primary) 06F07, 46M15 (Secondary)
dc.titleOn quantales and spectra of C*-algebras
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