Closed projections and peak interpolation for operator algebras

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dc.creatorHay, Damon M.
dc.date2005-12-15
dc.date2006-05-26
dc.date.accessioned2026-07-07T06:55:19Z
dc.date.available2026-07-07T06:55:19Z
dc.descriptionThe closed one-sided ideals of a C*-algebra are exactly the closed subspaces supported by the orthogonal complement of a closed projection. Let A be a (not necessarily selfadjoint) subalgebra of a unital C*-algebra B which contains the unit of B. Here we characterize the right ideals of A with left contractive approximate identity as those subspaces of A supported by the orthogonal complement of a closed projection in B** which also lies in the weak* closure of A. Although this seems quite natural, the proof requires a set of new techniques which may may be viewed as a noncommutative version of the subject of peak interpolation from the theory of function spaces. Thus, the right ideals with left approximate identity are closely related to a type of peaking phenomena in the algebra. In this direction we introduce a class of closed projections which generalizes the notion of a peak set in the theory of uniform algebras to the world of operator algebras and operator spaces.
dc.descriptiona minor correction to proposition 3.1 was made
dc.identifierhttps://arxiv.org/abs/math/0512353
dc.identifierhttp://arxiv.org/abs/math/0512353
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106244
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.subject46 (Primary) 47 (Secondary)
dc.titleClosed projections and peak interpolation for operator algebras
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