{
  "id": "1904.03252",
  "version": "v1",
  "published": "2019-04-05T19:52:39.000Z",
  "updated": "2019-04-05T19:52:39.000Z",
  "title": "(Non-)amenability of the Fourier algebra in the cb-multiplier norm",
  "authors": [
    "Volker Runde"
  ],
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "For a locally compact group $G$, let $A(G)$ denote its Fourier algebra, $M_{cb}(A(G))$ the completely bounded multipliers of $A(G)$, and $A_{Mcb}(G)$ the closure of $A(G)$ in $M_{cb}(A(G))$. We show that $A_{Mcb}(G)$ is not amenable if $G$ contains a copy of the free group in two generators as a closed subgroup.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-05T19:52:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46H20",
      "20E05",
      "22D05",
      "22D15",
      "43A22",
      "43A30",
      "47L25"
    ],
    "keywords": [
      "fourier algebra",
      "cb-multiplier norm",
      "amenability",
      "free group",
      "locally compact group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}