{
  "id": "0906.4196",
  "version": "v1",
  "published": "2009-06-23T09:11:09.000Z",
  "updated": "2009-06-23T09:11:09.000Z",
  "title": "A Banach-Stone theorem for Riesz isomorphisms of Banach lattices",
  "authors": [
    "Jin Xi Chen",
    "Zi Li Chen",
    "Ngai-Ching Wong"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X$ and $Y$ be compact Hausdorff spaces, and $E$, $F$ be Banach lattices. Let $C(X,E)$ denote the Banach lattice of all continuous $E$-valued functions on $X$ equipped with the pointwise ordering and the sup norm. We prove that if there exists a Riesz isomorphism $\\mathnormal{\\Phi}: C(X,E)\\to C(Y,F)$ such that $\\mathnormal{\\Phi}f$ is non-vanishing on $Y$ if and only if $f$ is non-vanishing on $X$, then $X$ is homeomorphic to $Y$, and $E$ is Riesz isomorphic to $F$. In this case, $\\mathnormal{\\Phi}$ can be written as a weighted composition operator: $\\mathnormal{\\Phi} f(y)=\\mathnormal{\\Pi}(y)(f(\\varphi(y)))$, where $\\varphi$ is a homeomorphism from $Y$ onto $X$, and $\\mathnormal{\\Pi}(y)$ is a Riesz isomorphism from $E$ onto $F$ for every $y$ in $Y$. This generalizes some known results obtained recently.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-23T09:11:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B42",
      "47B65"
    ],
    "keywords": [
      "banach lattice",
      "riesz isomorphism",
      "banach-stone theorem",
      "compact hausdorff spaces",
      "riesz isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.4196C"
    }
  }
}