Journal of Operator Theory

Volume 65, Issue 1, Winter 2011 pp. 131-144.

Purely infinite corona algebras of simple C$^*$-algebras with real rank zero

Authors: Dan Kucerovsky (1) and Francesc Perera (2)
Author institution: (1) Department of Mathematics, University of New Brunswick at Fredericton, Fredericton NB, E3B 5A3, Canada
(2) Departament de Matematiques, Universitat Autonoma de Barcelona, Bellaterra, Barcelona, 08193, Spain

Summary: In this paper we explore conditions on simple non-unital $C^*$-\break algebras with real rank zero and stable rank one under which their corona algebras are purely infinite and not necessarily simple. In particular, our results allow to characterize when the corona algebra of a simple AF-algebra is purely infinite in terms of continuity conditions on its scale.

Keywords: Corona algebras, purely infinite $C^*$-algebras, scales in $C^*$-algebras

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