{
  "id": "1401.5927",
  "version": "v2",
  "published": "2014-01-23T10:23:28.000Z",
  "updated": "2016-04-02T09:43:15.000Z",
  "title": "Asymptotic Behaviour and Cyclic Properties of Weighted Shifts on Directed Trees",
  "authors": [
    "György Pál Gehér"
  ],
  "comment": "22 pages",
  "journal": "Journal of Mathematical Analysis and Applications, 440 (2016), 14-32",
  "doi": "10.1016/j.jmaa.2016.03.019",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we investigate a new class of operators called weighted shifts on directed trees introduced recently in [Z. J. Jablonski, I. B. Jung and J. Stochel, A Non-hyponormal Operator Generating Stieltjes Moment Sequences, J. Funct. Anal. 262 (2012), no. 9, 3946--3980.]. This class is a natural generalization of the so called weighted bilateral, unilateral and backward shift operators. In the first part of the paper we calculate the asymptotic limit and the isometric asymptote of a contractive weighted shift on a directed tree and that of the adjoint. Then we use the asymptotic behaviour and similarity properties to deal with cyclicity. We also show that a weighted backward shift operator is cyclic if and only if there is at most one zero weight.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-23T10:23:28.000Z",
      "comment": "This article was submitted to a journal",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-04-02T09:43:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A16",
      "47B37"
    ],
    "keywords": [
      "directed tree",
      "weighted shift",
      "asymptotic behaviour",
      "cyclic properties",
      "backward shift operator"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.5927P"
    }
  }
}