Exactness of Cuntz-Pimsner C*-algebras

Abstract

Let H be a full Hilbert bimodule over a C*-algebra A. We show that the Cuntz-Pimsner C*-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 that 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.

21 pages

References in corpus (1)

• Embeddings of reduced free products of operator algebras

Cited by in corpus (7)

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• A look at the inner structure of the $2$-adic ring $C^{\ast }$-algebra and its automorphism groups
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• On a Notion of Exactness for Reduced Free Products of C*-Algebras
• Noncommutative pressure and the variational principle in Cuntz-Krieger-type C*-algebras
• Cuntz-Krieger-Pimsner Algebras Associated with Amalgamated Free Product Groups