{
  "id": "2002.09087",
  "version": "v1",
  "published": "2020-02-21T01:58:53.000Z",
  "updated": "2020-02-21T01:58:53.000Z",
  "title": "On a spectral mapping theorem for scalar type spectral operators, the weak spectral mapping theorem for and stability of $C_0$-semigroups of such operators",
  "authors": [
    "Marat V. Markin"
  ],
  "categories": [
    "math.FA",
    "math.SP"
  ],
  "abstract": "We prove a spectral mapping theorem for scalar type spectral operators and apply it to extend the weak spectral mapping theorem and the generalized Lyapunov stability theorem, known to hold for the $C_0$-semigroups of normal operators on complex Hilbert spaces, to the more general case of $C_0$-semigroups of scalar type spectral operators on complex Banach spaces. We also establish for the latter an analogue of the Gearhart-Pr\\\"uss-Greiner characterization of the uniform exponential stability for $C_0$-semigroups on complex Hilbert spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-21T01:58:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B40",
      "47D03",
      "47D60",
      "47D06",
      "47D99",
      "37C75",
      "47B15",
      "34G10",
      "34D20"
    ],
    "keywords": [
      "scalar type spectral operators",
      "weak spectral mapping theorem",
      "semigroups",
      "complex hilbert spaces",
      "generalized lyapunov stability theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}