{
  "id": "1401.2680",
  "version": "v3",
  "published": "2014-01-12T22:48:17.000Z",
  "updated": "2015-01-01T19:43:45.000Z",
  "title": "Spectra of Composition Operators with Symbols in S(2)",
  "authors": [
    "Paul S. Bourdon"
  ],
  "comment": "19 pages, 1 figure, to appear in the Journal of Operator Theory",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let H^2(D) denote the classical Hardy space of the open unit disk D in the complex plane. We obtain descriptions of both the spectrum and essential spectrum of composition operators on H^2(D) whose symbols belong to the class S(2) introduced by Kriete and Moorhouse [Trans. Amer. Math. Soc., 359, 2007]. Our work reveals new possibilities for the shapes of composition-operator spectra, settling a conjecture of Cowen's [J. Operator Th. 9, 1983]. Our results depend on a number of lemmas, perhaps of independent interest, that provide spectral characterizations of sums of elements of a unital algebra over a field when certain pairwise products of the summands are zero.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-20T01:33:08.000Z",
      "comment": "19 pages, 1 figure, improved, submitted for publication",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-01-01T19:43:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B33",
      "47A10"
    ],
    "keywords": [
      "composition operators",
      "open unit disk",
      "complex plane",
      "classical hardy space",
      "symbols belong"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.2680B"
    }
  }
}