Exactness of Cuntz-Pimsner C*-algebras

Citation
Kj. Dykema et D. Shlyakhtenko, Exactness of Cuntz-Pimsner C*-algebras, P EDIN MATH, 44, 2001, pp. 425-444
Citations number
34
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
ISSN journal
00130915 → ACNP
Volume
44
Year of publication
2001
Part
2
Pages
425 - 444
Database
ISI
SICI code
0013-0915(200106)44:<425:EOCC>2.0.ZU;2-N
Abstract
Let H be a full Hilbert bimodule over a C*-algebra A. We show that the Cunt z-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 amalgamat ed free products of exact C*-algebras. In the case in which A is a finite-d imensional C*-algebra, we also show that the Brown-Voiculescu topological e ntropy of Bogljubov automorphisms of the Cuntz-Pimsner algebra associated t o an A, A Hilbert bimodule is zero.