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Journal of Operator Theory

Volume 38, Issue 1, Summer 1997  pp. 131-149.

Extremal richness of multiplier algebras and corona algebras of simple C*-algebras

Authors: Nadia S. Larsen (1) and Hiroyuki Osaka (2)
Author institution:(1) Mathematics Institute, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen Ø, DENMARK
(2) Department of Mathematical Sciences, Ryukyu University, Nishihara-cho, Okinawa 903-01, JAPAN

Summary: A simple unital C*-algebra A is called extremally rich if the set of one-sided invertible elements is dense in A. We determine some conditions on a separable, simple, infinite dimensional C*-algebra of real rank zero under which we can decide whether the multiplier algebras M(A), $M(A \otimes K)$ and the corona algebras Q(A), $Q(A \otimes K)$ are extremally rich or not. Our analysis will depend on the existence of a finite trace for A and, when A is an AF algebra, on the number of infinite extremal traces of A and $A \otimes K$.

Keywords: Simple C*-algebras, extremal richness, real rank, stable rank.

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