2012/06/18 by David Peter Blecher, Blecher, David Peter, Charles John Read +1
Mathematics · #46H10 #46L07 #46L52 #47L30 #47L50 #47L55 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 46L85 #Secondary 32T40 #math.FA #math.OA #msc:32T40 #msc:46H10 #msc:46L07 #msc:46L52 #msc:46L85 #msc:47L30 #msc:47L50 #msc:47L55
paper · pdf · doi:10.48550/arxiv.1206.4022
18 pages. To appear J. Functional Analysis
arxiv created 2012/11/20 · arxiv updated 2012/11/21
We make several contributions to our recent program investigating structural properties of algebras of operators on a Hilbert space. For example, we make substantial contributions to the noncommutative peak interpolation program begun by Hay and the first author, Hay and Neal. Another sample result: an operator algebra has a contractive approximate identity iff the linear span of the elements with positive real part is dense. We also extend the theory of compact projections to the most general case. Despite the title, our algebras are often allowed to have no approximate identity.