{
  "id": "2010.04039",
  "version": "v1",
  "published": "2020-10-08T15:06:07.000Z",
  "updated": "2020-10-08T15:06:07.000Z",
  "title": "Koplienko-Neidhardt trace formula for unitaries $-$ A new proof",
  "authors": [
    "Arup Chattopadhyay",
    "Soma Das",
    "Chandan Pradhan"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Koplienko \\cite{Ko} found a trace formula for perturbations of self-adjoint operators by operators of Hilbert-Schmidt class $\\mathcal{B}_2(\\mathcal{H})$. Later in 1988, a similar formula was obtained by Neidhardt \\cite{NH} in the case of unitary operators. In this article, we give a still another proof of Koplienko-Neidhardt trace formula in the case of unitary operators 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}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-08T15:06:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A55",
      "47A56",
      "47A13",
      "47B10"
    ],
    "keywords": [
      "koplienko-neidhardt trace formula",
      "unitary operators",
      "kreins trace formula",
      "similar formula",
      "hilbert-schmidt class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}