{
  "id": "1112.4884",
  "version": "v3",
  "published": "2011-12-20T23:31:36.000Z",
  "updated": "2012-07-11T16:17:36.000Z",
  "title": "Minimal and maximal $p$-operator space structures",
  "authors": [
    "Serap Oztop",
    "Nico Spronk"
  ],
  "comment": "10 pages, emphasis changed, since we discovered some key ideas are already known",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We show that $L^\\infty(\\mu)$, in its capacity as multiplication operators on $L^p(\\mu)$, is minimal as a $p$-operator space for a decomposable measure $\\mu$. We conclude that $L^1(\\mu)$ has a certain maximal type $p$-operator space structure which facilitates computations with $L^1(\\mu)$ and the projective tensor product.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-07-11T16:17:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L07",
      "47L25",
      "46G10"
    ],
    "keywords": [
      "operator space structure",
      "maximal type",
      "multiplication operators",
      "facilitates computations",
      "projective tensor product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.4884O"
    }
  }
}