Closed Projections and Approximate Identities for Operator Algebras
نویسنده
چکیده
Let A be a (not necessarily selfadjoint) subalgebra of a unital C-algebra B which contains the unit of B. The right ideals of A with left contractive approximate identity are characterized as those subspaces of A supported by the orthogonal complement of a closed projection in B which also lies in A. Although this seems quite natural, the nonselfadjointness requires us to develop some interpolation results for its proof. 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.
منابع مشابه
Closed Projections and Peak Interpolation for Operator Algebras
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 ...
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