{
  "id": "1008.3267",
  "version": "v1",
  "published": "2010-08-19T10:37:40.000Z",
  "updated": "2010-08-19T10:37:40.000Z",
  "title": "Hypercyclic operators on topological vector spaces",
  "authors": [
    "Stanislav Shkarin"
  ],
  "comment": "The paper is submitted to Journal of LMS",
  "doi": "10.1112/jlms/jdr082",
  "categories": [
    "math.FA"
  ],
  "abstract": "Bonet, Frerick, Peris and Wengenroth constructed a hypercyclic operator on the locally convex direct sum of countably many copies of the Banach space $\\ell_1$. We extend this result. In particular, we show that there is a hypercyclic operator on the locally convex direct sum of a sequence $\\{X_n\\}_{n\\in\\N}$ of Fr\\'echet spaces if and only if each $X_n$ is separable and there are infinitely many $n\\in\\N$ for which $X_n$ is infinite dimensional. Moreover, we characterize inductive limits of sequences of separable Banach spaces which support a hypercyclic operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-19T10:37:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hypercyclic operator",
      "topological vector spaces",
      "locally convex direct sum",
      "frechet spaces",
      "infinite dimensional"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.3267S"
    }
  }
}