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.
|Journal||Journal of Operator Theory|
|Publication status||Published - 1 Sep 1998|
- Extremal richness
- Real rank
- Refinement monoid
- Stable rank