{
  "id": "math/9201211",
  "version": "v1",
  "published": "1990-03-27T19:45:00.000Z",
  "updated": "1990-03-27T19:45:00.000Z",
  "title": "Nuclear operators on spaces of continuous vector-valued functions",
  "authors": [
    "Paulette Saab",
    "Brenda Smith"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\Omega$ be a compact Hausdorff space, let $E$ be a Banach space, and let $C(\\Omega, E)$ stand for the Banach space of all $E$-valued continuous functions on $\\Omega$ under supnorm. In this paper we study when nuclear operators on $C(\\Omega, E)$ spaces can be completely characterized in terms of properties of their representing vector measures. We also show that if $F$ is a Banach space and if $T:\\ C(\\Omega, E)\\rightarrow F$ is a nuclear operator, then $T$ induces a bounded linear operator $T^\\#$ from the space $C(\\Omega)$ of scalar valued continuous functions on $\\Omega$ into $\\slN(E,F)$ the space of nuclear operators from $E$ to $F$, in this case we show that $E^*$ has the Radon-Nikodym property if and only if $T^\\#$ is nuclear whenever $T$ is nuclear.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1990-03-27T19:45:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E40",
      "46G10",
      "47B10",
      "28B05",
      "28B20"
    ],
    "keywords": [
      "nuclear operator",
      "continuous vector-valued functions",
      "banach space",
      "compact hausdorff space",
      "bounded linear operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}