{
  "id": "0909.4854",
  "version": "v1",
  "published": "2009-09-26T11:07:15.000Z",
  "updated": "2009-09-26T11:07:15.000Z",
  "title": "Multi-norms and modules over group algebras",
  "authors": [
    "Paul Ramsden"
  ],
  "comment": "29 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let G be a locally compact group, and let 1 < p < \\infty. In this paper we investigate the injectivity of the left L^1(G)-module L^p(G). We define a family of amenability type conditions called (p,q)-amenability, for any 1 <= p <= q. For a general locally compact group G we show if L^p(G) is injective, then G must be (p,p)-amenable. For a discrete group G we prove that l^p(G) is injective if and only if G is (p,p)-amenable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-26T11:07:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46H25",
      "43A20"
    ],
    "keywords": [
      "group algebras",
      "multi-norms",
      "general locally compact group",
      "amenability type conditions",
      "discrete group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.4854R"
    }
  }
}