{
  "id": "1007.2994",
  "version": "v2",
  "published": "2010-07-18T12:07:10.000Z",
  "updated": "2010-08-10T16:52:47.000Z",
  "title": "Trace formulae for perturbations of class $\\bs{\\bS_m}$",
  "authors": [
    "Alexei Aleksandrov",
    "Vladimir Peller"
  ],
  "comment": "23 pages",
  "categories": [
    "math.FA",
    "math.CA",
    "math.CV",
    "math.SP"
  ],
  "abstract": "We obtain general trace formulae in the case of perturbation of self-adjoint operators by self-adjoint operators of class $\\bS_m$, where $m$ is a positive integer. In \\cite{PSS} a trace formula for operator Taylor polynomials was obtained. This formula includes the Livshits--Krein trace formula in the case $m=1$ and the Koplienko trace formula in the case $m=2$. We establish most general trace formulae in the case of perturbation of Schatten--von Neumann class $\\bS_m$. We also improve the trace formula obtained in \\cite{PSS} for operator Taylor polynomials and prove it for arbitrary functions in he Besov space $B_{\\be1}^m(\\R)$. We consider several other special cases of our general trace formulae. In particular, we establish a trace formula for $m$th order operator differences.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-08-10T16:52:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A55",
      "47B10"
    ],
    "keywords": [
      "general trace formulae",
      "perturbation",
      "operator taylor polynomials",
      "th order operator differences",
      "self-adjoint operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.2994A"
    }
  }
}