{
  "id": "1101.4320",
  "version": "v2",
  "published": "2011-01-22T20:32:59.000Z",
  "updated": "2012-02-27T20:51:36.000Z",
  "title": "Multi-norms and the injectivity of $L^p(G)$",
  "authors": [
    "H. Garth Dales",
    "Matthew Daws",
    "Hung Le Pham",
    "Paul Ramsden"
  ],
  "comment": "31 pages; minor typographical and mathematical corrections",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $G$ be a locally compact group, and take $p\\in(1,\\infty)$. We prove that the Banach left $L^1(G)$-module $L^p(G)$ is injective (if and) only if the group $G$ is amenable. Our proof uses the notion of multi-norms. We also develop the theory of multi-normed spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-27T20:51:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46H25",
      "43A20"
    ],
    "keywords": [
      "multi-norms",
      "injectivity",
      "banach left",
      "locally compact group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.4320D"
    }
  }
}