{
  "id": "1407.0525",
  "version": "v2",
  "published": "2014-07-02T11:36:47.000Z",
  "updated": "2014-09-14T14:17:22.000Z",
  "title": "Asymptotic limits of operators similar to normal operators",
  "authors": [
    "György Pál Gehér"
  ],
  "comment": "13 pages, accepted for publication in Proceedings of the AMS",
  "categories": [
    "math.FA"
  ],
  "abstract": "Sz.-Nagy's famous theorem states that a bounded operator $T$ which acts on a complex Hilbert space $\\mathcal{H}$ is similar to a unitary operator if and only if $T$ is invertible and both $T$ and $T^{-1}$ are power bounded. There is an equivalent reformulation of that result which considers the self-adjoint iterates of $T$ and uses a Banach limit $L$. In this paper first we present a generalization of the necessity part in Sz.-Nagy's result concerning operators that are similar to normal operators. In the second part we provide characterization of all possible strong operator topology limits of the self-adjoint iterates of those contractions which are similar to unitary operators and act on a separable infinite-dimensional Hilbert space. This strengthens Sz.-Nagy's theorem for contractions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-02T11:36:47.000Z",
      "title": "Generalization and strengthening of Sz.-Nagy's theorem",
      "abstract": "Sz.-Nagy's famous theorem states that a bounded operator $T$ which acts on a complex Hilbert space $\\mathcal{H}$ is similar to a unitary operator if and only if $T$ is invertible and both $T$ and $T^{-1}$ are power bounded. There is an equivalent reformulation of that result which considers the self-adjoint iterates of $T$ and uses a Banach limit $L$. In this paper first we present a generalization of Sz.-Nagy's result concerning operators that are similar to normal operators. In the second part we provide characterization of all possible strong operator topology limits of the self-adjoint iterates of those contractions which are similar to unitary operators and act on a separable infinite-dimensional Hilbert space. This strengthens Sz.-Nagy's theorem for contractions.",
      "comment": "14 pages, submitted to a journal",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-14T14:17:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B40",
      "47A45",
      "47B15"
    ],
    "keywords": [
      "generalization",
      "self-adjoint iterates",
      "unitary operator",
      "strong operator topology limits",
      "complex hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.0525P"
    }
  }
}