Operator Figa-Talamanca-Herz algebras
| dc.creator | Runde, Volker | |
| dc.date | 2001-11-20 | |
| dc.date | 2003-01-02 | |
| dc.date.accessioned | 2026-07-07T04:44:42Z | |
| dc.date.available | 2026-07-07T04:44:42Z | |
| dc.description | Let G be a locally compact group. We use the canonical operator space structure on the spaces $L^p(G)$ for $p \in [1,\infty]$ introduced by G. Pisier to define operator space analogues $OA_p(G)$ of the classical Figa-Talamanca-Herz algebras $A_p(G)$. If $p \in (1,\infty)$ is arbitrary, then $A_p(G) \subset OA_p(G)$ such that the inclusion is a contraction; if p = 2, then $OA_2(G) \cong A(G)$ as Banachspaces spaces, but not necessarily as operator spaces. We show that $OA_p(G)$ is a completely contractive Banach algebra for each $p \in (1,\infty)$, and that $OA_q(G) \subset OA_p(G)$ completely contractively for amenable $G$ if $1 < p \leq q \leq 2$ or $2 \leq q \leq p < \infty$. Finally, we characterize the amenability of G through the existence of a bounded approximate identity in $OA_p(G)$ for one (or equivalently for all) $p \in (1,\infty)$. | |
| dc.description | 20 pages; some typos eliminated | |
| dc.identifier | https://arxiv.org/abs/math/0111225 | |
| dc.identifier | http://arxiv.org/abs/math/0111225 | |
| dc.identifier | Studia Math. 155 (2003), 152-170 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62696 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 43A15, 43A30, 46B70, 46J99, 46L07, 47L25 (primary) | |
| dc.title | Operator Figa-Talamanca-Herz algebras | |
| dc.type | text |