Extremal richness of multiplier and corona algebras of simple C*-algebras with real rank zero

Details Extremal richness of multiplier and corona algebras of simple C*-algebras with real rank zero Extremal richness of multiplier and corona algebras of simple C*-algebras with real rank zero

1999-06-26

arxiv.org/abs/math/9906180v1

Mathematics

Operator Algebras

20 pages (revised 1999); to appear in Journal of Operator Theory

Scientific paper

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.

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