Cuntz semigroups of ideals and quotients and a generalized Kasparov Stabilization Theorem

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dc.creatorCiuperca, Alin
dc.creatorRobert, Leonel
dc.creatorSantiago, Luis
dc.date2007-10-31
dc.date.accessioned2026-07-07T08:39:39Z
dc.date.available2026-07-07T08:39:39Z
dc.descriptionLet A be a C*-algebra and I a closed two-sided ideal of A. We use the Hilbert C*-modules picture of the Cuntz semigroup to investigate the relations between the Cuntz semigroups of I, A and A/I. We obtain a relation on two elements of the Cuntz semigroup of A that characterizes when they are equal in the Cuntz semigroup of A/I. As a corollary, we show that the Cuntz semigroup functor is exact. Replacing the Cuntz equivalence relation of Hilbert modules by their isomorphism, we obtain a generalization of Kasparov's Stabilization theorem.
dc.identifierhttps://arxiv.org/abs/0710.5800
dc.identifierhttp://arxiv.org/abs/0710.5800
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141148
dc.subjectOperator Algebras
dc.subject46L08; 46L35
dc.titleCuntz semigroups of ideals and quotients and a generalized Kasparov Stabilization Theorem
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