{
  "id": "0707.3426",
  "version": "v1",
  "published": "2007-07-23T18:42:17.000Z",
  "updated": "2007-07-23T18:42:17.000Z",
  "title": "Reproducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators",
  "authors": [
    "Michael T. Jury"
  ],
  "comment": "9 pages, to appear in Proc. Amer. Math Soc",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that the norm of a weighted composition operator on the Hardy space H^2 of the disk is controlled by the norm of the weight function in the de Branges-Rovnyak space associated to the symbol of the composition operator. As a corollary we obtain a new proof of the boundedness of composition operators on H^2, and recover the standard upper bound for the norm. Similar arguments apply to weighted Bergman spaces. We also show that the positivity of a generalized de Branges-Rovnyak kernel is sufficient for the boundedness of a given composition operator on the standard functions spaces on the unit ball.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-23T18:42:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B33",
      "47B32",
      "46E22"
    ],
    "keywords": [
      "weighted composition operator",
      "branges-rovnyak space",
      "reproducing kernels",
      "standard upper bound",
      "standard functions spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.3426J"
    }
  }
}