{
  "id": "1007.1649",
  "version": "v2",
  "published": "2010-07-09T19:22:28.000Z",
  "updated": "2010-08-14T23:55:16.000Z",
  "title": "Lifting derivations and $n-$weak amenability of the second dual of a Banach algebra",
  "authors": [
    "S. Barootkoob",
    "H. R. Ebrahimi Vishki"
  ],
  "comment": "8 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that for $n\\geq 2$ the $n-$weak amenability of the second dual $\\A^{**}$ of a Banach algebra $\\A$ implies that of $\\A$. We also provide a positive answer for the case $n=1,$ which sharpens some older results. Our method of proof also provides a unified approach to give short proofs for some known results in the case where $n=1$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-08-14T23:55:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46H20",
      "46H25"
    ],
    "keywords": [
      "second dual",
      "weak amenability",
      "banach algebra",
      "lifting derivations",
      "short proofs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.1649B"
    }
  }
}