Exactness of Cuntz-Pimsner C*-algebras Academic Article

abstract

• AbstractLet $H$ be a full Hilbert bimodule over a $C^*$-algebra $A$. We show that the CuntzPimsner 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 BrownVoiculescu topological entropy of Bogljubov automorphisms of the CuntzPimsner algebra associated to an $A,A$ Hilbert bimodule is zero.AMS 2000 Mathematics subject classification: Primary 46L08. Secondary 46L09; 46L54

authors

• Dykema, Kenneth

published proceedings

• PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY

author list (cited authors)

• Dykema, K. J., & Shlyakhtenko, D.

citation count

• 17

complete list of authors

• Dykema, KJ||Shlyakhtenko, D

publication date

• June 2001

publisher

• Cambridge University Press (CUP)  Publisher

published in

• Proceedings of the Edinburgh Mathematical Society  Journal

keywords

• Bogljubov Automorphisms
• Exact C*-algebras
• Hilbert Bimodules
• Non-commutative Topological Entropy

Digital Object Identifier (DOI)

• 10.1017/S001309159900125X

start page

• 425

end page

• 444

volume

• 44

issue

• 2

URL

• http%3A%2F%2Fdx.doi.org%2F10.1017%2Fs001309159900125x