{
  "id": "1909.09500",
  "version": "v1",
  "published": "2019-09-20T13:35:40.000Z",
  "updated": "2019-09-20T13:35:40.000Z",
  "title": "On $n$th roots of normal operators",
  "authors": [
    "B. P. Duggal",
    "I. H. Kim"
  ],
  "comment": "9 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "For $n$-normal operators $A$ [2, 4, 5], equivalently $n$-th roots $A$ of normal Hilbert space operators, both $A$ and $A^*$ satisfy the Bishop--Eschmeier--Putinar property $(\\beta)_{\\epsilon}$, $A$ is decomposable and the quasi-nilpotent part $H_0(A-\\lambda)$ of $A$ satisfies $H_0(A-\\lambda)^{-1}(0)=(A-\\lambda)^{-1}(0)$ for every non-zero complex $\\lambda$. $A$ satisfies every Weyl and Browder type theorem, and a sufficient condition for $A$ to be normal is that either $A$ is dominant or $A$ is a class ${\\mathcal A}(1,1)$ operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-20T13:35:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A05",
      "47A55",
      "47A80",
      "47A10"
    ],
    "keywords": [
      "normal operators",
      "th roots",
      "normal hilbert space operators",
      "browder type theorem",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}