{
  "id": "math/0211284",
  "version": "v6",
  "published": "2002-11-18T23:27:16.000Z",
  "updated": "2004-04-28T17:40:39.000Z",
  "title": "Amenability and weak amenability of the Fourier algebra",
  "authors": [
    "Brian E. Forrest",
    "Volker Runde"
  ],
  "comment": "16 pages; some, hopefully clarifying revisions",
  "journal": "Math. Z. 250 (2005), 731-744",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Let $G$ be a locally compact group. We show that its Fourier algebra $A(G)$ is amenable if and only if $G$ has an abelian subgroup of finite index, and that its Fourier-Stieltjes algebra $B(G)$ is amenable if and only if $G$ has a compact, abelian subgroup of finite index. We then show that $A(G)$ is weakly amenable if the component of the identity of $G$ is abelian, and we prove some partial results towards the converse.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2004-04-28T17:40:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22D25",
      "22E99",
      "43A30",
      "46H20",
      "46H25",
      "47L50"
    ],
    "keywords": [
      "fourier algebra",
      "weak amenability",
      "abelian subgroup",
      "finite index",
      "partial results"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....11284F"
    }
  }
}