The completely bounded approximation property for extended Cuntz-Pimsner algebras
Kenneth J. Dykema, Roger R. Smith
Abstract
The extended Cuntz-Pimsner algebra E(H), introduced by Pimsner, is constructed from a Hilbert B,B-bimodule H over a C*-algebra B. In this paper we investigate the Haagerup invariant Λ(.) for these algebras, the main result being that Λ(E(H))=Λ(B) when H is full over B. In particular, E(H) has the completely bounded approximation property if and only if the same is true for B.
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