## Abstract

Let 1 < p < ∞. 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 algebra V N(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}(V N(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}(V N(G)). Finally, we show that if G is a countable discrete group having the approximation property and V N(G) has the QWEP, then L_{P}(V N(G)) has a very nice local structure; that is, it is a script C sign script O sign ℒ_{p}-space and has a completely bounded Schauder basis.

Original language | English (US) |
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Pages (from-to) | 313-341 |

Number of pages | 29 |

Journal | Duke Mathematical Journal |

Volume | 117 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2003 |

## ASJC Scopus subject areas

- Mathematics(all)

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