{
  "id": "1903.11153",
  "version": "v1",
  "published": "2019-03-26T21:01:33.000Z",
  "updated": "2019-03-26T21:01:33.000Z",
  "title": "A note on the common spectral properties for bounded linear operators",
  "authors": [
    "Hassane Zguitti"
  ],
  "comment": "9 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X$ and $Y$ be Banach spaces, $A\\,:\\,X\\rightarrow Y$ and $B,\\,C\\,:\\,Y\\rightarrow X$ be bounded linear operators. We prove that if $A(BA)^2=ABACA=ACABA=(AC)^2A,$ then $$\\sigma_{*}(AC)\\setminus\\{0\\}=\\sigma_{*}(BA)\\setminus\\{0\\}$$ where $\\sigma_*$ runs over a large of spectra originated by regularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-26T21:01:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "47A53",
      "47A55"
    ],
    "keywords": [
      "bounded linear operators",
      "common spectral properties",
      "banach spaces",
      "regularities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}