Spectral synthesis and topologies on ideal spaces for Banach *-algebras
| dc.creator | Feinstein, J. F. | |
| dc.creator | Kaniuth, E. | |
| dc.creator | Somerset, D. W. B. | |
| dc.date | 1999-09-29 | |
| dc.date | 1999-10-06 | |
| dc.date.accessioned | 2026-07-07T05:30:56Z | |
| dc.date.available | 2026-07-07T05:30:56Z | |
| dc.description | This paper continues the study of spectral synthesis and the topologies $τ_{\infty}$ and $τ_r$ on the ideal space of a Banach algebra, concentrating on the class of Banach $^*$-algebras, and in particular on $L^1$-group algebras. It is shown that if a group G is a finite extension of an abelian group then $τ_r$ is Hausdorff on the ideal space of $L^1(G)$ if and only if $L^1(G)$ has spectral synthesis, which in turn is equivalent to $G$ being compact. The result is applied to nilpotent groups, [FD]$^-$-groups, and Moore groups. An example is given of a non-compact, non-abelian group G for which $L^1(G)$ has spectral synthesis. It is also shown that if G is a non-discrete group then $τ_r$ is not Hausdorff on the ideal lattice of the Fourier algebra A(G). | |
| dc.description | 20 pages plain tex, minor amendments | |
| dc.identifier | https://arxiv.org/abs/math/9909173 | |
| dc.identifier | http://arxiv.org/abs/math/9909173 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79167 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46H10; 46K05;43A45;22D15 | |
| dc.title | Spectral synthesis and topologies on ideal spaces for Banach *-algebras | |
| dc.type | text |