{
  "id": "math/0508496",
  "version": "v1",
  "published": "2005-08-25T10:32:39.000Z",
  "updated": "2005-08-25T10:32:39.000Z",
  "title": "The Socle and finite dimensionality of some Banach algebras",
  "authors": [
    "Ali Ghaffari",
    "Ali Reza Medghalchi"
  ],
  "comment": "4 pages, no figures, no tables",
  "journal": "Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 3, August 2005, pp. 327-330",
  "categories": [
    "math.FA"
  ],
  "abstract": "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 $\\mu$ in $\\hbox{Soc}(L^{1}(G))$ such that $\\mu(G) \\neq 0$. 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-08-25T10:32:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A25",
      "46H15"
    ],
    "keywords": [
      "banach algebra",
      "finite dimensionality",
      "nonzero left ideal",
      "minimal left ideal",
      "main results"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......8496G"
    }
  }
}