{
  "id": "math/0409454",
  "version": "v3",
  "published": "2004-09-23T15:30:44.000Z",
  "updated": "2005-01-06T20:31:36.000Z",
  "title": "The amenability constant of the Fourier algebra",
  "authors": [
    "Volker Runde"
  ],
  "comment": "LaTeX2e; 11 pages; some more minor revisions",
  "journal": "Proc. Amer. Math. Soc. 134 (2006), 1473-1481",
  "categories": [
    "math.FA"
  ],
  "abstract": "For a locally compact group $G$, let $A(G)$ denote its Fourier algebra and $\\hat{G}$ its dual object, i.e. the collection of equivalence classes of unitary represenations of $G$. We show that the amenability constant of $A(G)$ is less than or equal to $\\sup \\{\\deg(\\pi) : \\pi \\in \\hat{G} \\}$ and that it is equal to one if and only if $G$ is abelian.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-01-06T20:31:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46H20",
      "20B99",
      "22D05",
      "22D10",
      "43A40",
      "46J10",
      "46J40",
      "46L07",
      "47L25",
      "47L50"
    ],
    "keywords": [
      "fourier algebra",
      "amenability constant",
      "locally compact group",
      "dual object",
      "equivalence classes"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9454R"
    }
  }
}