{
  "id": "1404.5822",
  "version": "v2",
  "published": "2014-04-23T13:41:47.000Z",
  "updated": "2014-07-12T12:13:49.000Z",
  "title": "The spectrum of the product of operators, and the product of their numerical ranges",
  "authors": [
    "Chi-Kwong Li",
    "Ming-Cheng Tsai",
    "Kuo-Zhong Wang",
    "Ngai-Ching Wong"
  ],
  "comment": "11 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that a compact operator $A$ is a multiple of a positive semi-definite operator if and only if $$ \\sigma(AB) \\subseteq \\overline{W(A)W(B)}, \\quad\\text{for all (rank one) operators $B$}. $$ An example of a normal operator is given to show that the equivalence conditions may fail in general. We then obtain conditions to identify other classes of operators $A$ so that equivalence conditions hold.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-12T12:13:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "47A12",
      "15A60"
    ],
    "keywords": [
      "numerical ranges",
      "equivalence conditions hold",
      "compact operator",
      "normal operator",
      "positive semi-definite operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.5822L"
    }
  }
}