{
  "id": "math/0107153",
  "version": "v1",
  "published": "2001-07-20T21:02:15.000Z",
  "updated": "2001-07-20T21:02:15.000Z",
  "title": "On factorization of operators through the spaces $l^p.$",
  "authors": [
    "Oleg I. Reinov"
  ],
  "comment": "8 pages, AMSTeX; for the next paper see math.FA/0107113",
  "journal": "Vestnik SPb GU, ser. Matematika, 2 (2000), 27-32 (in Russian)",
  "categories": [
    "math.FA"
  ],
  "abstract": "We give conditions on a pair of Banach spaces $X$ and $Y,$ under which each operator from $X$ to $Y,$ whose second adjoint factors compactly through the space $l^p,$ $1\\le p\\le+\\infty$, itself compactly factors through $l^p.$ The conditions are as follows: either the space $X^*,$ or the space $Y^{***}$ possesses the Grothendieck approximation property. Leaving the corresponding question for parameters $p>1, p\\neq 2,$ still open, we show that for $p=1$ the conditions are essential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-07-20T21:02:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "factorization",
      "conditions",
      "grothendieck approximation property",
      "banach spaces",
      "second adjoint factors"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......7153R"
    }
  }
}