Approximation properties for noncommutative Lp-spaces associated with discrete groups

Marius Junge, Zhong Jin Ruan

Research output: Contribution to journalArticlepeer-review


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 Lp(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 Lp(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 Lp(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 LP(V N(G)) has a very nice local structure; that is, it is a script C sign script O sign ℒp-space and has a completely bounded Schauder basis.

Original languageEnglish (US)
Pages (from-to)313-341
Number of pages29
JournalDuke Mathematical Journal
Issue number2
StatePublished - Apr 1 2003

ASJC Scopus subject areas

  • Mathematics(all)


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