{
  "id": "math/0402018",
  "version": "v4",
  "published": "2004-02-03T14:40:57.000Z",
  "updated": "2004-10-20T19:21:22.000Z",
  "title": "Representations of locally compact groups on QSL_p-spaces and a p-analog of the Fourier-Stieltjes algebra",
  "authors": [
    "Volker Runde"
  ],
  "comment": "19 pages; LaTeX2e; two references added",
  "journal": "Pacific J. Math. 221 (2005), 379-397",
  "categories": [
    "math.FA",
    "math.RT"
  ],
  "abstract": "For a locally compact group $G$ and $p \\in (1,\\infty)$, we define $B_p(G)$ to be the space of all coefficient functions of isometric representations of $G$ on quotients of subspaces of $L_p$ spaces. For $p =2$, this is the usual Fourier--Stieltjes algebra. We show that $B_p(G)$ is a commutative Banach algebra that contractively (isometrically, if $G$ is amenable) contains the Fig\\`a-Talamanca--Herz algebra $A_p(G)$. If $2 \\leq q \\leq p$ or $p \\leq q \\leq 2$, we have a contractive inclusion $B_q(G) \\subset B_p(G)$. We also show that $B_p(G)$ embeds contractively into the multiplier algebra of $A_p(G)$ and is a dual space. For amenable $G$, this multiplier algebra and $B_p(G)$ are isometrically isomorphic.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2004-10-20T19:21:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46J99",
      "22D12",
      "22D35",
      "43A07",
      "43A15",
      "43A65",
      "46J99"
    ],
    "keywords": [
      "locally compact group",
      "multiplier algebra",
      "usual fourier-stieltjes algebra",
      "isometric representations",
      "commutative banach algebra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2018R"
    }
  }
}