{
  "id": "1407.1275",
  "version": "v1",
  "published": "2014-07-04T17:00:25.000Z",
  "updated": "2014-07-04T17:00:25.000Z",
  "title": "Characterisation of Cesàro and $L$-Asymptotic Limits of Matrices",
  "authors": [
    "György Pál Gehér"
  ],
  "comment": "15 pages, Linear and Multilinear Algebra(2014)",
  "doi": "10.1080/03081087.2014.899359",
  "categories": [
    "math.FA"
  ],
  "abstract": "The main goal of this paper is to characterise all the possible Ces\\`aro and $L$-asymptotic limits of powerbounded, complex matrices. The investigation of the $L$-asymptotic limit of a powerbounded operator goes back to Sz.-Nagy and it shows how the orbit of a vector behaves with respect to the powers. It turns out that the two types of asymptotic limits coincide for every powerbounded matrix and a special case is connected to the description of the products $SS^*$ where $S$ runs through those invertible matrices which have unit columnvectors. We also show that for any powerbounded operator acting on an arbitrary complex Hilbert space the norm of the $L$-asymptotic limit is greater than or equal to 1, unless it is zero; moreover, the same is true for the Ces\\`aro asymptotic limit of a not necessarily powerbounded operator, if it exists.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-04T17:00:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A45",
      "47B65"
    ],
    "keywords": [
      "powerbounded operator",
      "characterisation",
      "arbitrary complex hilbert space",
      "asymptotic limits coincide",
      "special case"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.1275P"
    }
  }
}