{
  "id": "math/0503093",
  "version": "v1",
  "published": "2005-03-05T09:12:11.000Z",
  "updated": "2005-03-05T09:12:11.000Z",
  "title": "Derivation into duals of ideals of Banach algebras",
  "authors": [
    "M E Gorgi",
    "T Yazdanpanah"
  ],
  "comment": "10 pages",
  "journal": "Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 4, November 2004, pp. 399-408",
  "categories": [
    "math.FA"
  ],
  "abstract": "We introduce two notions of amenability for a Banach algebra $\\cal A$. Let $I$ be a closed two-sided ideal in $\\cal A$, we say $\\cal A$ is $I$-weakly amenable if the first cohomology group of $\\cal A$ with coefficients in the dual space $I^*$ is zero; i.e., $H^1({\\cal A},I^*)=\\{0\\}$, and, $\\cal A$ is ideally amenable if $\\cal A$ is $I$-weakly amenable for every closed two-sided ideal $I$ in $\\cal A$. We relate these concepts to weak amenability of Banach algebras. We also show that ideal amenability is different from amenability and weak amenability. We study the $I$-weak amenability of a Banach algebra $\\cal A$ for some special closed two-sided\\break ideal $I$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-05T09:12:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "banach algebra",
      "weak amenability",
      "derivation",
      "closed two-sided ideal",
      "first cohomology group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3093G"
    }
  }
}