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EXACTNESS OF CUNTZ–PIMSNER C*-ALGEBRAS

Published online by Cambridge University Press:  20 January 2009

Kenneth J. Dykema  and
Dimitri Shlyakhtenko
Kenneth J. Dykema
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843–3368, USA (Ken.Dykema@math.tamu.edu)
Dimitri Shlyakhtenko
Affiliation:
Department of Mathematics, University of California, 405 Hilgard Avenue, Los Angeles, CA 90095-1555, USA (shlyakht@math.ucla.edu)
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Abstract

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Let $H$ be a full Hilbert bimodule over a $C^*$-algebra $A$. We show that the Cuntz–Pimsner algebra associated to $H$ is exact if and only if $A$ is exact. Using this result, we give alternative proofs for exactness of reduced amalgamated free products of exact $C^*$-algebras. In the case in which $A$ is a finite-dimensional $C^*$-algebra, we also show that the Brown–Voiculescu topological entropy of Bogljubov automorphisms of the Cuntz–Pimsner algebra associated to an $A,A$ Hilbert bimodule is zero.

AMS 2000 Mathematics subject classification: Primary 46L08. Secondary 46L09; 46L54

Keywords

Hilbert bimodulesnon-commutative topological entropyexact $C^*$-algebrasBogljubov automorphisms
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 2 , June 2001 , pp. 425 - 444
Copyright
Copyright © Edinburgh Mathematical Society 2001