Ideals and hereditary subalgebras in operator algebras
Tom 212 / 2012
Studia Mathematica 212 (2012), 65-93
MSC: Primary 46H10, 46L07, 47L30, 46L52; Secondary 16D70, 47L25, 47L40.
DOI: 10.4064/sm212-1-5
Streszczenie
This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach-algebraic point of view. Namely, we mainly investigate topics concerned with the ideal structure, and hereditary subalgebras (or HSA's, which are in some sense a generalization of ideals). Second, we study properties of operator algebras which are hereditary subalgebras in their bidual, or equivalently which are `weakly compact'. We also give several examples answering natural questions that arise in such an investigation.
