{
  "id": "2009.08977",
  "version": "v1",
  "published": "2020-09-18T17:18:54.000Z",
  "updated": "2020-09-18T17:18:54.000Z",
  "title": "On the spectral $ν$-continuity",
  "authors": [
    "Salvador Sánchez-Perales",
    "Sergio Palafox",
    "Tomás Pérez-Becerra"
  ],
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "In this paper we study the $\\nu$-continuity of the spectrum and some of its parts. We show that the approximate point spectrum $\\sigma_{ap}$ is upper semi-$\\nu$-continuous at every Fredholm operator, then we give sufficient conditions to guarantee the $\\nu$-continuity of $\\sigma_{ap}$. Also we show that the restriction of the Weyl spectrum on the class of essentially $G_1$ operators is $\\nu$-continuous. Finally, we investigate the $\\nu$-continuity of the spectrum on the class of $p$-hyponormal operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-18T17:18:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "47A53"
    ],
    "keywords": [
      "continuity",
      "approximate point spectrum",
      "sufficient conditions",
      "weyl spectrum",
      "fredholm operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}