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• W1988821410 endingPage "512" @default.
• W1988821410 startingPage "491" @default.
• W1988821410 abstract "The 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 $$ A^{{ bot bot }} $$ . Although this seems quite natural, the proof requires a set of new techniques which 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." @default.
• W1988821410 created "2016-06-24" @default.
• W1988821410 creator A5059918361 @default.
• W1988821410 date "2006-12-26" @default.
• W1988821410 modified "2023-10-09" @default.
• W1988821410 title "Closed Projections and Peak Interpolation for Operator Algebras" @default.
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• W1988821410 doi "https://doi.org/10.1007/s00020-006-1471-z" @default.
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