Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T16:24:03.490Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected])
Dimitri Shlyakhtenko
Affiliation:
Department of Mathematics, University of California, 405 Hilgard Avenue, Los Angeles, CA 90095-1555, USA ([email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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