math

# Title: Approximation Properties for Non-commutative L_p-Spaces Associated with Discrete Groups

Abstract: Let $1 < p < \infty$. It is shown that if $G$ is a discrete group with the approximation property introduced by Haagerup and Kraus, then the non-commutative $L_p(VN(G))$ space has the operator space approximation property. If, in addition, the group von Neumann algebra $VN(G)$ has the QWEP, i.e. is a quotient of a $C^*$-algebra with Lance's weak expectation property, then $L_p(VN(G))$ actually has the completely contractive approximation property and the approximation maps can be chosen to be finite-rank completely contractive multipliers on $L_p(VN(G))$. Finally, we show that if $G$ is a countable discrete group having the approximation property and $VN(G)$ has the QWEP, then $L_p(VN(G))$ has a very nice local structure, i.e. it is a $\mathcal C\OL_p$ space and has a completely bounded Schauder basis.
 Subjects: Operator Algebras (math.OA) MSC classes: 46L07, 46L51, 22D05 Cite as: arXiv:math/0206060 [math.OA] (or arXiv:math/0206060v1 [math.OA] for this version)

## Submission history

From: Marius Junge [view email]
[v1] Thu, 6 Jun 2002 22:34:00 GMT (21kb)

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