The Shilov boundary of an operator space - and the characterization theorems

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dc.creatorBlecher, David P.
dc.date1999-06-12
dc.date2000-12-05
dc.date.accessioned2026-07-07T05:29:28Z
dc.date.available2026-07-07T05:29:28Z
dc.descriptionWe study operator spaces, operator algebras, and operator modules, from the point of view of the `noncommutative Shilov boundary'. In this attempt to utilize some `noncommutative Choquet theory', we find that Hilbert C$^*-$modules and their properties, which we studied earlier in the operator space framework, replace certain topological tools. We introduce certain multiplier operator algebras and C$^*-$algebras of an operator space, which generalize the algebras of adjointable operators on a C$^*-$module, and the `imprimitivity C$^*-$algebra'. It also generalizes a classical Banach space notion. This multiplier algebra plays a key role here. As applications of this perspective, we unify, and strengthen several theorems characterizing operator algebras and modules, in a way that seems to give more information than other current proofs. We also include some general notes on the `commutative case' of some of the topics we discuss, coming in part from joint work with Christian Le Merdy, about `function modules'.
dc.descriptionThis is the final revised version
dc.identifierhttps://arxiv.org/abs/math/9906083
dc.identifierhttp://arxiv.org/abs/math/9906083
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78653
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.titleThe Shilov boundary of an operator space - and the characterization theorems
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