The Socle and finite dimensionality of some Banach algebras
| dc.creator | Ghaffari, Ali | |
| dc.creator | Medghalchi, Ali Reza | |
| dc.date | 2005-08-25 | |
| dc.date.accessioned | 2026-07-07T05:22:42Z | |
| dc.date.available | 2026-07-07T05:22:42Z | |
| dc.description | The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem~2 which states that for a locally compact group $G$, $G$ is compact if there exists a measure $μ$ in $\hbox{Soc}(L^{1}(G))$ such that $μ(G) \neq 0$. We also prove that $G$ is finite if $\hbox{Soc}(M(G))$ is closed and every nonzero left ideal in $M(G)$ contains a minimal left ideal. | |
| dc.description | 4 pages, no figures, no tables | |
| dc.identifier | https://arxiv.org/abs/math/0508496 | |
| dc.identifier | http://arxiv.org/abs/math/0508496 | |
| dc.identifier | Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 3, August 2005, pp. 327-330 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76159 | |
| dc.subject | Functional Analysis | |
| dc.subject | 22A25, 46H15 | |
| dc.title | The Socle and finite dimensionality of some Banach algebras | |
| dc.type | text |