Cohen-Host type idempotent theorems for representations on Banach spaces and applications to Figà-Talamanca-Herz algebras
| dc.creator | Runde, Volker | |
| dc.date | 2004-08-27 | |
| dc.date | 2006-05-08 | |
| dc.date.accessioned | 2026-07-07T07:44:44Z | |
| dc.date.available | 2026-07-07T07:44:44Z | |
| dc.description | Let $G$ be a locally compact group, and let ${\cal R}(G)$ denote the ring of subsets of $G$ generated by the left cosets of open subsets of $G$. The Cohen--Host idempotent theorem asserts that a set lies in ${\cal R}(G)$ if and only if its indicator function is a coefficient function of a unitary representation of $G$ on some Hilbert space. We prove related results for representations of $G$ on certain Banach spaces. We apply our Cohen--Host type theorems to the study of the Figà-Talamanca--Herz algebras $A_p(G)$ with $p \in (1,\infty)$. For arbitrary $G$, we characterize those closed ideals of $A_p(G)$ that have an approximate identity bounded by 1 in terms of their hulls. Furthermore, we characterize those $G$ such that $A_p(G)$ is 1-amenable for some -- and, equivalently, for all -- $p \in (1,\infty)$: these are precisely the abelian groups. | |
| dc.description | 20 pages; LaTeX2e; one reference exchanged | |
| dc.identifier | https://arxiv.org/abs/math/0408388 | |
| dc.identifier | http://arxiv.org/abs/math/0408388 | |
| dc.identifier | J. Math. Anal. Appl. 329 (2007), 736-751 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123304 | |
| dc.subject | Functional Analysis | |
| dc.subject | Primary 22D12; Secondary 22D05, 22D10, 43A07, 43A15, 43A30, 43A65, 46B08, 46B20, 46H20, 46H25, 46J10, 46J20, 46J40 | |
| dc.title | Cohen-Host type idempotent theorems for representations on Banach spaces and applications to Figà-Talamanca-Herz algebras | |
| dc.type | text |