Operator Segal Algebras in Fourier Algebras
| dc.creator | Forrest, Brian E. | |
| dc.creator | Spronk, Nico | |
| dc.creator | Wood, Peter J. | |
| dc.date | 2006-01-20 | |
| dc.date.accessioned | 2026-07-07T09:40:27Z | |
| dc.date.available | 2026-07-07T09:40:27Z | |
| dc.description | Let G be a locally compact group, A(G) its Fourier algebra and L1(G) the space of Haar integrable functions on G. We study the Segal algebra SA(G)=A(G)\cap L1(G) in A(G). It admits an operator space structure which makes it a completely contractive Banach algebra. We compute the dual space of SA(G). We use it show that restriction operator u|->u|H:SA(G)->A(H), for some non-open closed subgroups H, is a surjective complete qutient map. We also show that if N is a non-compact closed subgroup, then the averaging operator tau_N:SA(G)->L1(G/N), tau_N u(sN)=\int_N u(sn)dn is a surjective complete quotient map. This puts an operator space perspective on the philosophy that SA(G) is ``locally A(G) while globally L1''. Also, using the operator space structure we can show that SA(G) is operator amenable exactly when when G is compact; and we can show that it is always operator weakly amenable. To obtain the latter fact, we use E. Samei's theory of hyper-Tauberian Banach algebras. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0601509 | |
| dc.identifier | http://arxiv.org/abs/math/0601509 | |
| dc.identifier | Studia Math. 179 (2007), no. 3, 277--295. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161493 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 43A30; 46L07; 43A07; 47L25 | |
| dc.title | Operator Segal Algebras in Fourier Algebras | |
| dc.type | text |