{
  "id": "math/0601509",
  "version": "v1",
  "published": "2006-01-20T19:19:07.000Z",
  "updated": "2006-01-20T19:19:07.000Z",
  "title": "Operator Segal Algebras in Fourier Algebras",
  "authors": [
    "Brian E. Forrest",
    "Nico Spronk",
    "Peter J. Wood"
  ],
  "comment": "20 pages",
  "journal": "Studia Math. 179 (2007), no. 3, 277--295.",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Let G be a locally compact group, A(G) its Fourier algebra and L1(G) the space of Haar integrable functions on G. We study the Segal algebra SA(G)=A(G)\\cap L1(G) in A(G). It admits an operator space structure which makes it a completely contractive Banach algebra. We compute the dual space of SA(G). We use it show that restriction operator u|->u|H:SA(G)->A(H), for some non-open closed subgroups H, is a surjective complete qutient map. We also show that if N is a non-compact closed subgroup, then the averaging operator tau_N:SA(G)->L1(G/N), tau_N u(sN)=\\int_N u(sn)dn is a surjective complete quotient map. This puts an operator space perspective on the philosophy that SA(G) is ``locally A(G) while globally L1''. Also, using the operator space structure we can show that SA(G) is operator amenable exactly when when G is compact; and we can show that it is always operator weakly amenable. To obtain the latter fact, we use E. Samei's theory of hyper-Tauberian Banach algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-01-20T19:19:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A30",
      "46L07",
      "43A07",
      "47L25"
    ],
    "keywords": [
      "operator segal algebras",
      "fourier algebra",
      "operator space structure",
      "surjective complete quotient map",
      "closed subgroup"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1509F"
    }
  }
}