{
  "id": "0809.3278",
  "version": "v3",
  "published": "2008-09-19T02:15:43.000Z",
  "updated": "2022-07-18T20:01:22.000Z",
  "title": "Isometries and spectra of multiplication operators on the Bloch space",
  "authors": [
    "Robert F. Allen",
    "Flavia Colonna"
  ],
  "journal": "Bull. Aust. Math. Soc. 79 (2009), no. 1, 147--160",
  "doi": "10.1017/S0004972708001196",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those induced by constant functions of modulus 1. We then describe the spectrum of the multiplication operators in terms of the range of the symbol. Lastly, we identify the isometries and spectra of a particular class of weighted composition operators on the Bloch space.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-10-31T16:23:38.000Z",
      "comment": "accepted to the Bulletin of the Australian Mathematical Society",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2022-07-18T20:01:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B38",
      "30D45"
    ],
    "keywords": [
      "bloch space",
      "weighted composition operators",
      "isometries",
      "isometric multiplication operators",
      "unit disk"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.3278A"
    }
  }
}