{
  "id": "1901.00310",
  "version": "v1",
  "published": "2019-01-02T10:01:24.000Z",
  "updated": "2019-01-02T10:01:24.000Z",
  "title": "Which multiplication operators are surjective isometries?",
  "authors": [
    "Eugene Bilokopytov"
  ],
  "comment": "17 pages, preliminary version",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\mathbf{F}$ be a Banach space of continuous functions over a connected locally compact space $X$. We present several sufficient conditions on $\\mathbf{F}$ guaranteeing that the only multiplication operators on $\\mathbf{F}$ that are surjective isometries are scalar multiples of the identity. The conditions are given via the properties of the inclusion operator from $\\mathbf{F}$ into $\\mathcal{C}\\left(X\\right)$, as well as in terms of geometry on $\\mathbf{F}$. An important tool in our investigation is the notion of Birkhoff Orthogonality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-02T10:01:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiplication operators",
      "surjective isometries",
      "banach space",
      "important tool",
      "inclusion operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}