{
  "id": "1504.05242",
  "version": "v1",
  "published": "2015-04-20T21:43:57.000Z",
  "updated": "2015-04-20T21:43:57.000Z",
  "title": "Criterion for $\\mathbb{Z}_d$--symmetry of a Spectrum of a Compact Operator",
  "authors": [
    "Boris S. Mityagin"
  ],
  "comment": "11 pages, no figures",
  "categories": [
    "math.FA",
    "math.SP"
  ],
  "abstract": "If $A$ is a compact operator in a Banach space and some power $A^q$ is nuclear we give a criterion of $\\mathbb{Z}_{d}$ -- symmetry of its spectrum $\\sigma{A}$ in terms of vanishing of the traces $\\mathop{\\mathit{Trace}} A^n$ for all $n$, $n \\geq 0$, $n \\neq 0 \\mod d$, sufficiently large.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-20T21:43:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B10",
      "47B07",
      "47B40"
    ],
    "keywords": [
      "compact operator",
      "banach space",
      "sufficiently large"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150405242M"
    }
  }
}