{
  "id": "0808.1858",
  "version": "v1",
  "published": "2008-08-13T16:20:33.000Z",
  "updated": "2008-08-13T16:20:33.000Z",
  "title": "Weak amenability of Fourier algebras on compact groups",
  "authors": [
    "Brian E. Forrest",
    "Ebrahim Samei",
    "Nico Spronk"
  ],
  "comment": "14 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We give for a compact group G, a full characterisation of when its Fourier algebra A(G) is weakly amenable: when the connected component of the identity G_e is abelian. This condition is also equivalent to the hyper-Tauberian property for A(G), and to having the anti-diagonal D^v={(s,s^{-1}):s is in G} being a set of spectral synthesis for A(GXG). We show the relationship between amenability and weak amenability of A(G), and (operator) amenability and (operator) weak amenability of A_D(G), an algebra defined by the authors in arXiv:0705.4277. We close by extending our results to some classes of non-compact, locally compact groups, including small invariant neighbourhood groups and maximally weakly almost periodic groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-13T16:20:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A30",
      "43A77",
      "46M20",
      "47L25",
      "46J10"
    ],
    "keywords": [
      "weak amenability",
      "fourier algebra",
      "small invariant neighbourhood groups",
      "periodic groups",
      "locally compact groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.1858F"
    }
  }
}