Operator space structure on Feichtinger's Segal algebra
| dc.creator | Spronk, Nico | |
| dc.date | 2006-07-12 | |
| dc.date | 2007-05-29 | |
| dc.date.accessioned | 2026-07-07T09:40:28Z | |
| dc.date.available | 2026-07-07T09:40:28Z | |
| dc.description | We extend the definition, from the class of abelian groups to a general locally compact group G, of Feichtinger's remarkable Segal algebra S_0(G). In order to obtain functorial properties for non-abelain groups, in particular a tensor product formula, we endow S_0(G) with an operator space structure. With this structure S_0(G) is simultaneously an operator Segal algebra of the Fourier algebra A(G), and of the group algebra L^1(G). We show that this operator space structure is consistent with the major functorial properties: (i) S_0(G)\hat{\otimes}S_0(H)=S_0(G\times H) completely isomorphically (operator projective tensor product), if H is another locally compact group; (ii) the restriction map u\mapsto u|_H:S_0(G)\to S_0(H) is completely surjective, if H is a closed subgroup; and (iii) T_N:S_0(G)\to S_0(G/N) is completely surjective, where N is a normal subgroup and T_N u(sN)=\int_N u(sn)dn. We also show that S_0(G) is an invariant for G when it is treated simultaneously as a pointwise algebra and a convolutive algebra. | |
| dc.description | 25 pages. Proof of Theorem 3.1 repaired. DOI included | |
| dc.identifier | https://arxiv.org/abs/math/0607299 | |
| dc.identifier | http://arxiv.org/abs/math/0607299 | |
| dc.identifier | J. Funct. Anal. 248 (2007), no. 1, 152--174. | |
| dc.identifier | doi:10.1016/j.jfa.2007.03.028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161494 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 43A30, 43A20, 46L07; 47L25, 46M05 | |
| dc.title | Operator space structure on Feichtinger's Segal algebra | |
| dc.type | text |