Crossed products of operator spaces

Abstract

Let $V$ be an operator space and $\iso(V)$ be the group of all completely isometric bijective linear mappings on $V$. Let $G$ act on $V$ via a strongly continuous group homomorphism $α:G \to \iso (V)$. We define the full (and reduced) operator space crossed product $V\rtimes^{\op}_{α,(r)}G$ and show that for a $C^{\ast }$-algebra with its canonical operator space structure, it coincides with the corresponding $C^{\ast }$-algebra crossed product. Unfortunately, the proof of Theorem 4.3 of the paper contains a serious gap, which leads to the withdrawal of the paper.

This paper has been withdrawn by the authors due to a serious gap in the proof of Theorem 4.3 which is crucial for the rest of the paper. The authors plan to publish part of the results in a different publication

References in corpus (1)

• Expanders, exact crossed products, and the Baum-Connes conjecture