{
  "id": "math/0310151",
  "version": "v3",
  "published": "2003-10-10T17:00:48.000Z",
  "updated": "2004-06-01T17:52:59.000Z",
  "title": "A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal",
  "authors": [
    "Volker Runde"
  ],
  "comment": "16 pages; some more, minor revisions",
  "journal": "Trans. Amer. Math. Soc. 358 (2006), 391-402",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Let $G$ be a locally compact group, and let $WAP(G)$ denote the space of weakly almost periodic functions on $G$. We show that, if $G$ is a $[SIN]$-group, but not compact, then the dual Banach algebra $WAP(G)^\\ast$ does not have a normal, virtual diagonal. Consequently, whenever $G$ is an amenable, non-compact $[SIN]$-group, $WAP(G)^\\ast$ is an example of a Connes-amenable, dual Banach algebra without a normal,virtual diagonal.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-06-01T17:52:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A15",
      "22A20",
      "43A07",
      "43A10",
      "43A60",
      "46H20",
      "46H25",
      "46M18",
      "46M20"
    ],
    "keywords": [
      "dual banach algebra",
      "virtual diagonal",
      "connes-amenable",
      "locally compact group",
      "periodic functions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10151R"
    }
  }
}