{
  "id": "1111.4475",
  "version": "v2",
  "published": "2011-11-18T20:48:16.000Z",
  "updated": "2012-04-12T13:48:22.000Z",
  "title": "Perturbation theory for normal operators",
  "authors": [
    "Armin Rainer"
  ],
  "comment": "32 pages, Remark 7.5 on m-sectorial operators added, accepted for publication in Trans. Amer. Math. Soc",
  "journal": "Trans. Amer. Math. Soc., 365 (2013), 5545--5577",
  "doi": "10.1090/S0002-9947-2013-05854-0",
  "categories": [
    "math.FA",
    "math.AG"
  ],
  "abstract": "Let $E \\ni x\\mapsto A(x)$ be a $\\mathscr{C}$-mapping with values unbounded normal operators with common domain of definition and compact resolvent. Here $\\mathscr{C}$ stands for $C^\\infty$, $C^\\omega$ (real analytic), $C^{[M]}$ (Denjoy--Carleman of Beurling or Roumieu type), $C^{0,1}$ (locally Lipschitz), or $C^{k,\\alpha}$. The parameter domain $E$ is either $\\mathbb R$ or $\\mathbb R^n$ or an infinite dimensional convenient vector space. We completely describe the $\\mathscr{C}$-dependence on $x$ of the eigenvalues and the eigenvectors of $A(x)$. Thereby we extend previously known results for self-adjoint operators to normal operators, partly improve them, and show that they are best possible. For normal matrices $A(x)$ we obtain partly stronger results.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-12T13:48:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26C10",
      "26E10",
      "32B20",
      "47A55"
    ],
    "keywords": [
      "perturbation theory",
      "infinite dimensional convenient vector space",
      "values unbounded normal operators",
      "compact resolvent",
      "partly stronger results"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.4475R"
    }
  }
}