{
  "id": "2010.14740",
  "version": "v1",
  "published": "2020-10-28T04:16:28.000Z",
  "updated": "2020-10-28T04:16:28.000Z",
  "title": "Asymptotic limits, Banach limits, and Cesàro means",
  "authors": [
    "C. S. Kubrusly",
    "B. P. Duggal"
  ],
  "journal": "Advances in Mathematical Sciences and Applications, Vol. 29, no. 1, pp. 145-170, Oct. 2020",
  "categories": [
    "math.FA"
  ],
  "abstract": "Every new inner product in a Hilbert space is obtained from the original one by means of a unique positive operator$.$ The first part of the paper is a survey on applications of such a technique, including a characterization of similarity to isometries$.$ The second part focuses on Banach limits for dealing with power bounded operators. It is shown that if a power bounded operator for which the sequence of shifted Ces\\`aro means converges (at least in the weak topology) uniformly in the shift parameter, then it has a Ces\\`aro asymptotic limit coinciding with its $\\varphi$-asymptotic limit for all Banach limits $\\varphi$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-28T04:16:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A30",
      "47A45",
      "47A62",
      "47B20"
    ],
    "keywords": [
      "banach limits",
      "asymptotic limit",
      "cesàro means",
      "power bounded operator",
      "second part focuses"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}