{
  "id": "1611.02981",
  "version": "v1",
  "published": "2016-11-07T14:41:15.000Z",
  "updated": "2016-11-07T14:41:15.000Z",
  "title": "Representation for bounded linear operator on Hilbert spaces",
  "authors": [
    "Luo Lvlin"
  ],
  "comment": "10pages. arXiv admin note: substantial text overlap with arXiv:1503.06750",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we construct some $C^{*}$-algebra induced by polar decomposition $T=U|T|$. We get that $T$ is unitary equivalent to $\\sqrt{|\\eta|}M_{z\\phi}$ on $\\mathcal{L}^{2}(\\sigma(|T|),\\mu_{|T|})$, where $\\phi\\in\\mathcal{L}^{\\infty}(\\sigma(|T|),\\mu_{|T|})$ and $\\eta\\in\\mathcal{L}^{1}(\\sigma(|T|),\\mu_{|T|})$. Also, we get that $T$ is normal if and only if $T$ is unitary equivalent to $M_{z\\phi}$ on $\\mathcal{L}^{2}(\\sigma(|T|),\\mu_{|T|})$, and if and only if $T\\in\\mathcal{A}^{'}(|T|)$, where $\\phi\\in\\mathcal{L}^{\\infty}(\\sigma(|T|),\\mu_{|T|})$ and $\\mathcal{A}^{'}(|T|)$ is the commutant of $\\mathcal{A}(|T|)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-07T14:41:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B99",
      "46L05",
      "47A65",
      "47A67"
    ],
    "keywords": [
      "bounded linear operator",
      "hilbert spaces",
      "representation",
      "unitary equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}