{
  "id": "1901.02737",
  "version": "v1",
  "published": "2019-01-09T13:37:54.000Z",
  "updated": "2019-01-09T13:37:54.000Z",
  "title": "Surjective isometries on a Banach space of analytic functions on the open unit disc",
  "authors": [
    "Takeshi Miura"
  ],
  "comment": "46 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $H(\\mathbb{D})$ be the linear space of all analytic functions on the open unit disc $\\mathbb{D}$. We define $\\mathcal{S}^\\infty$ by the linear subspace of all $f \\in H(\\mathbb{D})$ with bounded derivative $f'$ on $\\mathbb{D}$. We give the characterization of surjective, not necessarily linear, isometries on $\\mathcal{S}^\\infty$ with respect to the following two norms: $\\| f \\|_\\infty + \\| f' \\|_\\infty$ and $|f(a)| + \\| f' \\|_\\infty$ for $a \\in \\mathbb{D}$, where $\\| \\cdot \\|_\\infty$ is the supremum norm on $\\mathbb{D}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-09T13:37:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46J10"
    ],
    "keywords": [
      "open unit disc",
      "analytic functions",
      "banach space",
      "surjective isometries",
      "linear space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}