{
  "id": "math/0501092",
  "version": "v3",
  "published": "2005-01-06T20:39:01.000Z",
  "updated": "2005-05-08T15:14:29.000Z",
  "title": "Operator amenability of the Fourier algebra in the cb-multiplier norm",
  "authors": [
    "Brian E. Forrest",
    "Volker Runde",
    "Nico Spronk"
  ],
  "comment": "LaTeX2e; 18 pages; cleaned up a bit",
  "journal": "Canadian J. Math. 59 (2007), 966-980",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Let $G$ be a locally compact group, and let $A_\\cb(G)$ denote the closure of $A(G)$, the Fourier algebra of $G$, in the space of completely bounded multipliers of $A(G)$. If $G$ is a weakly amenable, discrete group such that $\\cstar(G)$ is residually finite-dimensional, we show that $A_\\cb(G)$ is operator amenable. In particular, $A_\\cb(F_2)$ is operator amenable even though $F_2$, the free group in two generators, is not an amenable group. Moreover, we show that, if $G$ is a discrete group such that $A_\\cb(G)$ is operator amenable, a closed ideal of $A(G)$ is weakly completely complemented in $A(G)$ if and only if it has an approximate identity bounded in the cb-multiplier norm.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-05-08T15:14:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A22",
      "43A30",
      "46H25",
      "46J10",
      "46J40",
      "46L07",
      "47L25"
    ],
    "keywords": [
      "fourier algebra",
      "cb-multiplier norm",
      "operator amenability",
      "discrete group",
      "operator amenable"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1092F"
    }
  }
}