2005/12/17 by David P. Blecher, Damon M. Hay, Blecher, David P. +4 · 3 citations
Mathematics · #46A55 #46L07 #46L08 #46L30 #46L85 #47L30 #47L50 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 46H10 #Secondary 32T40 #math.FA #math.OA #msc:32T40 #msc:46A55 #msc:46H10 #msc:46L07 #msc:46L08 #msc:46L30 #msc:46L85 #msc:47L30 #msc:47L50
paper · pdf · doi:10.48550/arxiv.math/0512417
Final version, To appear. 21 pages
openalex publication_date 2005/12/17 · arxiv created 2006/03/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In recent work of the second author, a technical result was proved establishing a bijective correspondence between certain open projections in a C*-algebra containing an operator algebra A, and certain one-sided ideals of A. Here we give several remarkable consequences of this result. These include a generalization of the theory of hereditary subalgebras of a C*-algebra, and the solution of a ten year old problem on the Morita equivalence of operator algebras. In particular, the latter gives a very clean generalization of the notion of Hilbert C*-modules to nonselfadjoint algebras. We show that an `ideal' of a general operator space X is the intersection of X with an `ideal' in any containing C*-algebra or C*-module. Finally, we discuss the noncommutative variant of the classical theory of `peak sets'.