{
  "id": "2104.08864",
  "version": "v1",
  "published": "2021-04-18T14:17:07.000Z",
  "updated": "2021-04-18T14:17:07.000Z",
  "title": "Koplienko trace formula for unitaries via linear path",
  "authors": [
    "Arup Chattopadhyay",
    "Soma Das",
    "Chandan Pradhan"
  ],
  "comment": "24 pages, Submitted to Journal. arXiv admin note: text overlap with arXiv:2010.04039",
  "categories": [
    "math.FA"
  ],
  "abstract": "Koplienko \\cite{Ko} found a trace formula for perturbations of self-adjoint operators by operators of Hilbert-Schmidt class $\\mathcal{B}_2(\\mathcal{H})$. In 2012, Potapov and Sukochev \\cite{PoSu} obtained a similar formula for pairs of contractions by answering an open question posed by Gesztesy, Pushnitski, and Simon in \\cite[Open Question 11.2]{GePu}. In this article, we give a still another proof of the Koplienko trace formula in the case of unitary operators via linear path by reducing the problem to a finite-dimensional one as in the proof of Krein's trace formula by Voiculescu \\cite{Voi}, Sinha and Mohapatra \\cite{MoSi94,MoSi96}. Consequently, we obtain the Koplienko trace formula for a class of pairs of contractions using the Sch$\\ddot{a}$ffer matrix unitary dilation. Moreover, we also obtain the Koplienko trace formula for a pair of self-adjoint operators and maximal dissipative operators using the Cayley transform.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-18T14:17:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A55",
      "47A56",
      "47A13",
      "47B10"
    ],
    "keywords": [
      "koplienko trace formula",
      "linear path",
      "ffer matrix unitary dilation",
      "self-adjoint operators",
      "kreins trace formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}