{
  "id": "1906.03613",
  "version": "v1",
  "published": "2019-06-09T10:41:37.000Z",
  "updated": "2019-06-09T10:41:37.000Z",
  "title": "The spectrum of composition operators induced by a rotation in the space of all analytic functions on the disc",
  "authors": [
    "José Bonet"
  ],
  "comment": "6 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "A characterization of those points in the unit disc which belong to the spectrum of a composition operator $C_{\\varphi}$, defined by a rotation $\\varphi(z)=rz$ with $|r|=1$, on the space $H_0(\\mathbb{D})$ of all analytic functions on the unit disc which vanish at $0$, is given. Examples show that the point $1$ may or may not belong to the spectrum of $C_{\\varphi}$, and this is related to Diophantine approximation. Our results complement recent work by Arendt, Celari\\`es and Chalendar.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-09T10:41:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B33",
      "47A10",
      "46E10",
      "11K60"
    ],
    "keywords": [
      "composition operator",
      "analytic functions",
      "unit disc",
      "diophantine approximation",
      "results complement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}