{
  "id": "1307.1000",
  "version": "v1",
  "published": "2013-07-03T13:07:51.000Z",
  "updated": "2013-07-03T13:07:51.000Z",
  "title": "Extreme non-Arens regularity of the group algebra",
  "authors": [
    "Mahmoud Filali",
    "Jorge Galindo"
  ],
  "categories": [
    "math.FA",
    "math.GN",
    "math.GR",
    "math.OA"
  ],
  "abstract": "Following Granirer, a Banach algebra A is extremely non-Arens regular when the quotient space A*/WAP(A) contains a closed linear subspace which has A* as a continuous linear image. We prove that the group algebra L^1(G) of any infinite locally compact group is always extremely non-Arens regular. When G is not discrete, this result is deduced from the much stronger property that, in fact, there is a linear isometric copy of L^\\infty(G) in the quotient space L^\\infty(G)/CB(G), where CB(G) stands for the algebra of all continuous and bounded functions on G.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-03T13:07:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22D15",
      "43A46",
      "43A15",
      "43A60",
      "54H11"
    ],
    "keywords": [
      "extreme non-arens regularity",
      "group algebra",
      "extremely non-arens regular",
      "quotient space",
      "infinite locally compact group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.1000F"
    }
  }
}