{
  "id": "1708.00724",
  "version": "v1",
  "published": "2017-08-02T12:46:52.000Z",
  "updated": "2017-08-02T12:46:52.000Z",
  "title": "Canonical decomposition of operators associated with the symmetrized polydisc",
  "authors": [
    "Sourav Pal"
  ],
  "comment": "11 pages, submitted",
  "categories": [
    "math.FA"
  ],
  "abstract": "A tuple of commuting operators $(S_1,\\dots,S_{n-1},P)$ for which the closed symmetrized polydisc $\\Gamma_n$ is a spectral set is called a $\\Gamma_n$-contraction. We show that every $\\Gamma_n$-contraction admits a decomposition into a $\\Gamma_n$-unitary and a completely non-unitary $\\Gamma_n$-contraction. This decomposition is an analogue to the canonical decomposition of a contraction into a unitary and a completely non-unitary contraction. We also find new characterizations for the set $\\Gamma_n$ and $\\Gamma_n$-contractions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-02T12:46:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "canonical decomposition",
      "contraction admits",
      "spectral set",
      "non-unitary contraction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}