{
  "id": "math/0610171",
  "version": "v1",
  "published": "2006-10-05T16:24:17.000Z",
  "updated": "2006-10-05T16:24:17.000Z",
  "title": "Derivations into n-th duals of ideals of Banach algebras",
  "authors": [
    "M. Eshaghi Gordji",
    "R. Memarbashi"
  ],
  "comment": "11 page",
  "categories": [
    "math.FA"
  ],
  "abstract": "We introduce two notions of amenability for a Banach algebra $\\cal A$. Let $n\\in \\Bbb N$ and let $I$ be a closed two-sided ideal in $\\cal A$, $\\cal A$ is $n-I-$weakly amenable if the first cohomology group of $\\cal A$ with coefficients in the n-th dual space $I^{(n)}$ is zero; i.e., $H^1({\\cal A},I^{(n)})=\\{0\\}$. Further, $\\cal A$ is n-ideally amenable if $\\cal A$ is $n-I-$weakly amenable for every closed two-sided ideal $I$ in $\\cal A$. We find some relationships of $n-I-$ weak amenability and $m-J-$ weak amenability for some different m and n or for different closed ideals $I$ and $J$ of $\\cal A$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-05T16:24:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46H25"
    ],
    "keywords": [
      "banach algebra",
      "derivations",
      "weak amenability",
      "closed two-sided ideal",
      "n-th dual space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10171E"
    }
  }
}