{
  "id": "1804.04884",
  "version": "v1",
  "published": "2018-04-13T11:02:43.000Z",
  "updated": "2018-04-13T11:02:43.000Z",
  "title": "A hypercyclicity criterion for non-metrizable topological vector spaces",
  "authors": [
    "Alfred Peris"
  ],
  "comment": "5 pages (to appear in Functiones et Approximatio Commentarii Mathematici)",
  "categories": [
    "math.FA",
    "math.DS"
  ],
  "abstract": "We provide a sufficient condition for an operator $T$ on a non-metrizable and sequentially separable topological vector space $X$ to be sequentially hypercyclic. This condition is applied to some particular examples, namely, a composition operator on the space of real analytic functions on $]0,1[$, which solves two problems of Bonet and Doma\\'nski \\cite{bd12}, and the \"snake shift\" constructed in \\cite{bfpw} on direct sums of sequence spaces. The two examples have in common that they do not admit a densely embedded F-space $Y$ for which the operator restricted to $Y$ is continuous and hypercyclic, i.e., the hypercyclicity of these operators cannot be a consequence of the comparison principle with hypercyclic operators on F-spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-13T11:02:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A16"
    ],
    "keywords": [
      "non-metrizable topological vector spaces",
      "hypercyclicity criterion",
      "real analytic functions",
      "sufficient condition",
      "hypercyclic operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}