{
  "id": "1302.1736",
  "version": "v1",
  "published": "2013-02-07T12:58:18.000Z",
  "updated": "2013-02-07T12:58:18.000Z",
  "title": "Dynamics of perturbations of the identity operator by multiples of the backward shift on $l^{\\infty}(\\mathbb{N})$",
  "authors": [
    "George Costakis",
    "Antonios Manoussos",
    "Amir Bahman Nasseri"
  ],
  "comment": "12 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $B$, $I$ be the unweighted backward shift and the identity operator respectively on $l^{\\infty}(\\mathbb{N})$, the space of bounded sequences over the complex numbers endowed with the supremum norm. We prove that $I+\\lambda B$ is locally topologically transitive if and only if $|\\lambda |>2$. This, shows that a classical result of Salas, which says that backward shift perturbations of the identity operator are always hypercyclic, or equivalently topologically transitive, on $l^p(\\mathbb{N})$, $1\\leq p<+\\infty$, fails to hold for the notion of local topological transitivity on $l^{\\infty}(\\mathbb{N})$. We also obtain further results which complement certain results from \\cite{CosMa}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-07T12:58:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A16"
    ],
    "keywords": [
      "supremum norm",
      "backward shift perturbations",
      "local topological transitivity",
      "complement",
      "complex numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.1736C"
    }
  }
}