Hereditary subalgebras of operator algebras

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dc.creatorBlecher, David P.
dc.creatorHay, Damon M.
dc.creatorNeal, Matthew
dc.date2005-12-17
dc.date2006-03-17
dc.date.accessioned2026-07-07T06:55:27Z
dc.date.available2026-07-07T06:55:27Z
dc.descriptionIn recent work of the second author, a technical result was proved establishing a bijective correspondence between certain open projections in a C*-algebra containing an operator algebra A, and certain one-sided ideals of A. Here we give several remarkable consequences of this result. These include a generalization of the theory of hereditary subalgebras of a C*-algebra, and the solution of a ten year old problem on the Morita equivalence of operator algebras. In particular, the latter gives a very clean generalization of the notion of Hilbert C*-modules to nonselfadjoint algebras. We show that an `ideal' of a general operator space X is the intersection of X with an `ideal' in any containing C*-algebra or C*-module. Finally, we discuss the noncommutative variant of the classical theory of `peak sets'.
dc.descriptionFinal version, To appear. 21 pages
dc.identifierhttps://arxiv.org/abs/math/0512417
dc.identifierhttp://arxiv.org/abs/math/0512417
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106286
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.subjectPrimary 46H10, 46L07, 46L85, 47L30, Secondary 32T40, 46A55, 46L08, 46L30, 47L50
dc.titleHereditary subalgebras of operator algebras
dc.typetext

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