{
  "id": "1802.08098",
  "version": "v1",
  "published": "2018-02-22T15:25:50.000Z",
  "updated": "2018-02-22T15:25:50.000Z",
  "title": "Bloch functions on the unit ball of a Banach space",
  "authors": [
    "Alejandro Miralles"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions $f$ on the unit ball $B_E$ of finite and infinite dimensional complex Banach spaces in two different ways: by extending the classical Bloch space considering the boundness of $(1-\\|x\\|^2) \\|f'(x)\\|$ on $B_E$ and by preserving the invariance of the correspondiing seminorm when we compose with automorphisms $\\phi$ of $B_E$. We study the connection between these spaces proving that they are different in general and prove that all bounded analytic functions on $B_{E}$ are Bloch functions in both ways.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-22T15:25:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unit ball",
      "infinite dimensional complex banach spaces",
      "analytic functions",
      "considering bloch functions",
      "bounded symmetric domains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}