{
  "id": "1006.2121",
  "version": "v1",
  "published": "2010-06-10T19:17:36.000Z",
  "updated": "2010-06-10T19:17:36.000Z",
  "title": "Compact differences of composition operators",
  "authors": [
    "Katherine Heller",
    "Barbara D. MacCluer",
    "Rachel J. Weir"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "When $\\varphi$ and $\\psi$ are linear-fractional self-maps of the unit ball $B_N$ in ${\\mathbb C}^N$, $N\\geq 1$, we show that the difference $C_{\\varphi}-C_{\\psi}$ cannot be non-trivially compact on either the Hardy space $H^2(B_N)$ or any weighted Bergman space $A^2_{\\alpha}(B_N)$. Our arguments emphasize geometrical properties of the inducing maps $\\varphi$ and $\\psi$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-10T19:17:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B33"
    ],
    "keywords": [
      "composition operators",
      "compact differences",
      "unit ball",
      "linear-fractional self-maps",
      "hardy space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.2121H"
    }
  }
}