{
  "id": "1205.0414",
  "version": "v1",
  "published": "2012-05-02T12:58:44.000Z",
  "updated": "2012-05-02T12:58:44.000Z",
  "title": "Hypercyclic operators on countably dimensional spaces",
  "authors": [
    "Andre Schenke",
    "Stanislav Shkarin"
  ],
  "categories": [
    "math.FA",
    "math.DS"
  ],
  "abstract": "According to Grivaux, the group $GL(X)$ of invertible linear operators on a separable infinite dimensional Banach space $X$ acts transitively on the set $\\Sigma(X)$ of countable dense linearly independent subsets of $X$. As a consequence, each $A\\in \\Sigma(X)$ is an orbit of a hypercyclic operator on $X$. Furthermore, every countably dimensional normed space supports a hypercyclic operator. We show that for a separable infinite dimensional Fr\\'echet space $X$, $GL(X)$ acts transitively on $\\Sigma(X)$ if and only if $X$ possesses a continuous norm. We also prove that every countably dimensional metrizable locally convex space supports a hypercyclic operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-02T12:58:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hypercyclic operator",
      "countably dimensional spaces",
      "infinite dimensional banach space",
      "infinite dimensional frechet space",
      "dimensional normed space supports"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.0414S"
    }
  }
}