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

M. Junge; Z. -J. Ruan

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

算子代数 2007-05-23 v1

作者: M. Junge , Z. -J. Ruan

摘要

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.

关键词

lp spaces and inequalities lie groups

引用

@article{arxiv.math/0206060,
  title  = {Approximation Properties for Non-commutative L_p-Spaces Associated with Discrete Groups},
  author = {M. Junge and Z. -J. Ruan},
  journal= {arXiv preprint arXiv:math/0206060},
  year   = {2007}
}

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

摘要

关键词

引用

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