{
  "id": "0909.4695",
  "version": "v2",
  "published": "2009-09-25T13:20:29.000Z",
  "updated": "2014-04-30T14:27:40.000Z",
  "title": "Rigidity of contractions on Hilbert spaces",
  "authors": [
    "Tanja Eisner"
  ],
  "comment": "17 pages. The results of this paper are published in Section IV.3 in the author's monograph \"Stability of Operators and Operator Semigroups\", Springer Verlag",
  "categories": [
    "math.FA",
    "math.DS"
  ],
  "abstract": "We study the asymptotic behaviour of contractive operators and strongly continuous semigroups on separable Hilbert spaces using the notion of rigidity. In particular, we show that a \"typical\" contraction $T$ contains the unit circle times the identity operator in the strong limit set of its powers, while $T^{n_j}$ converges weakly to zero along a sequence $\\{n_j\\}$ with density one. The continuous analogue is presented for isometric ang unitary $C_0$-(semi)groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-30T14:27:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A35",
      "28D05"
    ],
    "keywords": [
      "contraction",
      "unit circle times",
      "strong limit set",
      "isometric ang unitary",
      "asymptotic behaviour"
    ],
    "tags": [
      "monograph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.4695E"
    }
  }
}