Operator amenability of the Fourier algebra in the cb-multiplier norm
| dc.creator | Forrest, Brian E. | |
| dc.creator | Runde, Volker | |
| dc.creator | Spronk, Nico | |
| dc.date | 2005-01-06 | |
| dc.date | 2005-05-08 | |
| dc.date.accessioned | 2026-07-07T08:35:35Z | |
| dc.date.available | 2026-07-07T08:35:35Z | |
| dc.description | Let $G$ be a locally compact group, and let $A_\cb(G)$ denote the closure of $A(G)$, the Fourier algebra of $G$, in the space of completely bounded multipliers of $A(G)$. If $G$ is a weakly amenable, discrete group such that $\cstar(G)$ is residually finite-dimensional, we show that $A_\cb(G)$ is operator amenable. In particular, $A_\cb(F_2)$ is operator amenable even though $F_2$, the free group in two generators, is not an amenable group. Moreover, we show that, if $G$ is a discrete group such that $A_\cb(G)$ is operator amenable, a closed ideal of $A(G)$ is weakly completely complemented in $A(G)$ if and only if it has an approximate identity bounded in the cb-multiplier norm. | |
| dc.description | LaTeX2e; 18 pages; cleaned up a bit | |
| dc.identifier | https://arxiv.org/abs/math/0501092 | |
| dc.identifier | http://arxiv.org/abs/math/0501092 | |
| dc.identifier | Canadian J. Math. 59 (2007), 966-980 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139795 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | Primary 43A22; Secondary 43A30, 46H25, 46J10, 46J40, 46L07, 47L25 | |
| dc.title | Operator amenability of the Fourier algebra in the cb-multiplier norm | |
| dc.type | text |