2013/09/08 by David P. Blecher, Blecher, David P., C. J. Read +2
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.FA #math.OA #msc:43A45 #msc:46B15 #msc:46B28 #msc:46J10 #msc:46J40 #msc:47L30 #msc:47L55
paper · pdf · doi:10.48550/arxiv.1309.2023
28 pages, to appear Transactions American Math. Society
arxiv created 2014/10/25 · arxiv updated 2014/10/28
We exhibit a singly generated, semisimple commutative operator algebra with a contractive approximate identity, such that the spectrum of the generator is a null sequence and zero, but the algebra is not the closed linear span of the idempotents associated with the null sequence and obtained from the analytic functional calculus. Moreover the multiplication on the algebra is neither compact nor weakly compact. Thus we construct a `large' operator algebra of orthogonal idempotents, which may be viewed as a dense subalgebra of c0.