Completely Bounded Homomorphisms of the Fourier Algebras
| dc.creator | Ilie, M. | |
| dc.creator | Spronk, N. | |
| dc.date | 2004-05-04 | |
| dc.date | 2004-07-30 | |
| dc.date.accessioned | 2026-07-07T06:21:53Z | |
| dc.date.available | 2026-07-07T06:21:53Z | |
| dc.description | For locally compact groups G and H let A(G) denote the Fourier algebra of G and B(H) the Fourier-Stieltjes algebra of H. Any continuous piecewise affine map alpha:Y -> G (where Y is an element of the open coset ring of H) induces a completely bounded homomorphism Phi_alpha:A(G) -> B(H) by setting Phi_alpha u(.)=u(alpha(.)) on Y and Phi_alpha u=0 off of Y. We show that if G is amenable then any completely bounded homomorphism Phi:A(G) -> B(H) is of this form; and this theorem fails if G contains a discrete nonabelian free group. Our result generalises results of P.J. Cohen, B. Host and of the first author. We also obtain a description of all the idempotents in the Fourier-Stieltjes algebras which are contractive or positive definite. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0405063 | |
| dc.identifier | http://arxiv.org/abs/math/0405063 | |
| dc.identifier | J. Func. Anal. 225 (2):480-499, 2005. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95742 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 43A30; 46L07; 22D25; 47B65 | |
| dc.title | Completely Bounded Homomorphisms of the Fourier Algebras | |
| dc.type | text |