{
  "id": "1304.6193",
  "version": "v5",
  "published": "2013-04-23T07:52:42.000Z",
  "updated": "2013-08-26T14:30:24.000Z",
  "title": "Notes on C_0-representations and the Haagerup property",
  "authors": [
    "Paul Jolissaint"
  ],
  "comment": "Notes partly of an expository nature; 11 pages; a few typos fixed; final version to appear in the Bulletin of the Belgian Mathematical Society - Simon Stevin",
  "categories": [
    "math.GR"
  ],
  "abstract": "For any locally compact group $G$, we show the existence and uniqueness up to quasi-equivalence of a unitary $C_0$-representation $\\pi_0$ of $G$ such that all coefficient functions of $C_0$-representations of $G$ are coefficient functions of $\\pi_0$. The present work, strongly influenced by the work of N. Brown and E. Guentner (which dealt exclusively with discrete groups), leads to new characterizations of the Haagerup property: if $G$ is second countable, then it has that property if and only if the representation $\\pi_0$ induces a *-isomorphism of $C^*(G)$ onto $C^*_{\\pi_0}(G)$. When $G$ is discrete, we also relate the Haagerup property to relative strong mixing properties of the group von Neumann algebra $L(G)$ into finite von Neumann algebras.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-08-26T14:30:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22D10",
      "22D25",
      "46L10"
    ],
    "keywords": [
      "haagerup property",
      "finite von neumann algebras",
      "group von neumann algebra",
      "coefficient functions",
      "representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.6193J"
    }
  }
}