{
  "id": "math/0512044",
  "version": "v3",
  "published": "2005-12-02T01:57:44.000Z",
  "updated": "2006-05-12T06:25:23.000Z",
  "title": "Compact weighted composition operators and fixed points in convex domains",
  "authors": [
    "Dana D. Clahane"
  ],
  "comment": "10 pages. Corrected a few typographical errors and an error in one step of the main result's proof. This paper was presented in September 2005 at the Wabash Extramural Modern Analysis Mini-conference in Indianapolis",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "We extend a classical result of Caughran/Schwartz and another recent result of Gunatillake by showing that if D is a bounded, convex domain in n-dimensional complex space, m is a holomorphic function on D and bounded away from zero toward the boundary of D, and p is a holomorphic self-map of D such that the weighted composition operator W assigning the product of m and the composition of f and p to a given function f is compact on a holomorphic functional Hilbert space (containing the polynomial functions densely) on D with reproducing kernel K blowing up along the diagonal of D toward its boundary, then p has a unique fixed point in D. We apply this result by making a reasonable conjecture about the spectrum of W based on previous one-variable and multivariable results concerning compact weighted and unweighted composition operators.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-05-12T06:25:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B33",
      "32A10"
    ],
    "keywords": [
      "compact weighted composition operators",
      "convex domain",
      "fixed point",
      "results concerning compact",
      "holomorphic functional hilbert space"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12044C"
    }
  }
}