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Information Center for Mathematical Science

논문검색

Duke Mathematical Journal
( Vol. 117 NO.2 / (2003))
Approximation Properties for Noncommutative $L_p$-Spaces Associated with Discrete Groups
Marius Junge, Zhong-Jin Ruan,
Pages. 313-341
Abstract Let $1 < p < infty$. It is shown that if $G$ is a discrete group with the approximation
property introduced by U. Haagerup and J. Kraus, then the noncommutative
$L_p(V N (G))$-space has the operator space approximation property. If, in addition,
the group von Neumann algebr $VN(G)$ has the quotient weak expectation property
(QWEP), that is, 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 ; that is, it is a $mathscr{C O L}_p$-space and has a
completely bounded Schauder basis.
Contents 1. Introduction
2. Preliminaries
3. Approximation properties for $L_p(V N(G))$
4. Completely contractive approximation property for $L_p(VN(G))$
5. Local structure and completely bounded Schauder basis
Key words
Mathmatical Subject Classification 46L07, 46L51, 22D05, 43A30