{
  "id": "math/9210206",
  "version": "v1",
  "published": "1992-10-08T15:45:24.000Z",
  "updated": "1992-10-08T15:45:24.000Z",
  "title": "Interpolation of compact operators by the methods of Calderón and Gustavsson-Peetre",
  "authors": [
    "Michael Cwikel",
    "Nigel J. Kalton"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $ X=(X_0,X_1)$ and $ Y=(Y_0,Y_1)$ be Banach couples and suppose $T: X\\to Y$ is a linear operator such that $T:X_0\\to Y_0$ is compact. We consider the question whether the operator $T:[X_0,X_1]_{\\theta}\\to [Y_0,Y_1]_{\\theta}$ is compact and show a positive answer under a variety of conditions. For example it suffices that $X_0$ be a UMD-space or that $X_0$ is reflexive and there is a Banach space so that $X_0=[W,X_1]_{\\alpha}$ for some $0<\\alpha<1.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "1992-10-08T15:45:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact operators",
      "interpolation",
      "gustavsson-peetre",
      "banach couples",
      "banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1992math.....10206C"
    }
  }
}