The completely bounded approximation property for extended Cuntz-Pimsner algebras

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 \Lambda(.) for these algebras, the main result being that \Lambda(E(H))=\Lambda(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.