{
  "id": "1209.0979",
  "version": "v1",
  "published": "2012-09-05T13:54:47.000Z",
  "updated": "2012-09-05T13:54:47.000Z",
  "title": "Mixing operators on spaces with weak topology",
  "authors": [
    "Stanislav Shkarin"
  ],
  "journal": "Demonstratio Math. 44 (2011), 143-150",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that a continuous linear operator $T$ on a topological vector space $X$ with weak topology is mixing if and only if the dual operator $T'$ has no finite dimensional invariant subspaces. This result implies the characterization of hypercyclic operators on the space $\\omega$ due to Herzog and Lemmert and implies the result of Bayart and Matheron, who proved that for any hypercyclic operator $T$ on $\\omega$, $T\\oplus T$ is also hypercyclic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-05T13:54:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A16",
      "37A25"
    ],
    "keywords": [
      "weak topology",
      "mixing operators",
      "hypercyclic operator",
      "finite dimensional invariant subspaces",
      "continuous linear operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.0979S"
    }
  }
}