{
  "id": "1009.0583",
  "version": "v3",
  "published": "2010-09-03T04:58:21.000Z",
  "updated": "2011-05-02T11:59:04.000Z",
  "title": "On tensor products of weak mixing vector sequences and their applications to uniquely $E$-weak mixing $C^*$- dynamical systems",
  "authors": [
    "Farrukh Mukhamedov"
  ],
  "comment": "14 pages",
  "journal": "Bull, Aus. Math. Soc. 85(2012), 46-59",
  "categories": [
    "math.FA",
    "math.DS"
  ],
  "abstract": "We prove that, under certain conditions, uniform weak mixing (to zero) of the bounded sequences in Banach space implies uniform weak mixing of its tensor product. Moreover, we prove that ergodicity of tensor product of the sequences in Banach space implies its weak mixing. Applications of the obtained results, we prove that tensor product of uniquely $E$-weak mixing $C^*$-dynamical systems is also uniquely $E$-weak mixing as well.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-05-02T11:59:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L35",
      "46L55",
      "46L51",
      "28D05"
    ],
    "keywords": [
      "weak mixing vector sequences",
      "tensor product",
      "dynamical systems",
      "implies uniform weak mixing",
      "banach space implies uniform weak"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.0583M"
    }
  }
}