{
  "id": "math/0107113",
  "version": "v1",
  "published": "2001-07-16T11:39:30.000Z",
  "updated": "2001-07-16T11:39:30.000Z",
  "title": "On linear operators with p-nuclear adjoints",
  "authors": [
    "Oleg I. Reinov"
  ],
  "comment": "6 pages, AMSTeX",
  "journal": "Vestnik SPb GU, ser. Matematika, 4 (2000), 24-27 (in Russia)",
  "categories": [
    "math.FA"
  ],
  "abstract": "If $p\\in [1,+\\infty]$ and $T$ is a linear operator with $p$-nuclear adjoint from a Banach space $ X$ to a Banach space $Y$ then if one of the spaces $X^*$ or $Y^{***}$ has the approximation property, then $T$ belongs to the ideal $N^p$ of operators which can be factored through diagonal oparators $l_{p'}\\to l_1.$ On the other hand, there is a Banach space $W$ such that $W^{**}$ has a basis and such that for each $p\\in [1,+\\infty], p\\neq 2,$ there exists an operator $T: W^{**}\\to W$ with $p$-nuclear adjoint that is not in the ideal $N^p,$ as an operator from $W^{**}$ to $ W.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-07-16T11:39:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear operator",
      "p-nuclear adjoints",
      "banach space",
      "diagonal oparators",
      "approximation property"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......7113R"
    }
  }
}