{
  "id": "1204.2044",
  "version": "v1",
  "published": "2012-04-10T05:05:04.000Z",
  "updated": "2012-04-10T05:05:04.000Z",
  "title": "Linear operators with wild dynamics",
  "authors": [
    "Jean-Matthieu Augé"
  ],
  "comment": "14 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "If $X$ is a separable infinite dimensional Banach space, we construct a bounded and linear operator $R$ on $X$ such that $$ A_R=\\{x \\in X, \\|R^tx\\| \\rightarrow \\infty\\} $$ is not dense and has non empty interior with the additional property that $R$ can be written $I+K$, where $I$ is the identity and $K$ is a compact operator. This answers two recent questions of H\\'ajek and Smith.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-10T05:05:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A05",
      "47A15",
      "47A16"
    ],
    "keywords": [
      "linear operator",
      "wild dynamics",
      "separable infinite dimensional banach space",
      "non empty interior",
      "compact operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2044A"
    }
  }
}