Closed projections and peak interpolation for operator algebras
摘要
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 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.
引用
@article{arxiv.math/0512353,
title = {Closed projections and peak interpolation for operator algebras},
author = {Damon M. Hay},
journal= {arXiv preprint arXiv:math/0512353},
year = {2007}
}
备注
a minor correction to proposition 3.1 was made