Approximation Properties for Non-commutative L_p-Spaces Associated with Discrete Groups
| dc.creator | Junge, M. | |
| dc.creator | Ruan, Z. -J. | |
| dc.date | 2002-06-06 | |
| dc.date.accessioned | 2026-07-07T04:48:56Z | |
| dc.date.available | 2026-07-07T04:48:56Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0206060 | |
| dc.identifier | http://arxiv.org/abs/math/0206060 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64239 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L07, 46L51, 22D05 | |
| dc.title | Approximation Properties for Non-commutative L_p-Spaces Associated with Discrete Groups | |
| dc.type | text |