1999/06/26 by Francesc Perera, Perera, Francesc
Mathematics · #06F05 #46L05 #46L80 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:06F05 #msc:46L05 #msc:46L80
paper · pdf · doi:10.48550/arxiv.math/9906180
20 pages (revised 1999); to appear in Journal of Operator Theory
arxiv created 1999/06/26 · arxiv updated 2009/11/30
In this paper we investigate the extremal richness of the multiplier algebra M(A) and the corona algebra M(A)/A, for a simple C*-algebra A with real rank zero and stable rank one. We show that the space of extremal quasitraces and the scale of A contain enough information to determine whether M(A)/A is extremally rich. In detail, if the scale is finite, then M(A)/A is extremally rich. In important cases, and if the scale is not finite, extremal richness is characterized by a restrictive condition: the existence of only one infinite extremal quasitrace which is isolated in a convex sense.