{
  "id": "1903.00522",
  "version": "v1",
  "published": "2019-03-01T20:17:19.000Z",
  "updated": "2019-03-01T20:17:19.000Z",
  "title": "Further common local spectral properties for bounded linear operators",
  "authors": [
    "Hassane Zguitti"
  ],
  "comment": "12 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this note, we study common local spectral properties for bounded linear operators $A\\in\\mathcal{L}(X,Y)$ and $B,C\\in\\mathcal{L}(Y,X)$ such that $$A(BA)^2=ABACA=ACABA=(AC)^2A.$$ We prove that $AC$ and $BA$ share the single valued extension property, the Bishop property $(\\beta)$, the property $(\\beta_{\\epsilon})$, the decomposition property $(\\delta)$ and decomposability. Closedness of analytic core and quasinilpotent part are also investigated. Some applications to Fredholm operators are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-01T20:17:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "47A11",
      "47A53",
      "47A55"
    ],
    "keywords": [
      "bounded linear operators",
      "study common local spectral properties",
      "single valued extension property",
      "analytic core",
      "decomposition property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}