{
  "id": "0904.1761",
  "version": "v1",
  "published": "2009-04-10T22:42:40.000Z",
  "updated": "2009-04-10T22:42:40.000Z",
  "title": "The behavior of functions of operators under perturbations",
  "authors": [
    "V. V. Peller"
  ],
  "comment": "37 pages",
  "categories": [
    "math.FA",
    "math.CA",
    "math.CV",
    "math.SP"
  ],
  "abstract": "This is a survey article. We consider different problems in connection with the behavior of functions of operators under perturbations of operators. We deal with three classes of operators: unitary operators, self-adjoint operators, and contractions. We study operator Lipschitz and operator differentiable functions. We also study the behavior of functions under perturbations of an operator by an operator of Schatten--von Neumann class $\\bS_p$ and apply the results to the Livschits--Krein and Koplienko--Neidhardt trace formulae. We also include in this survey article recent unexpected results obtained in a joint paper with Aleksandrov on operator H\\\"older--Zygmund functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-10T22:42:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A55",
      "47B49",
      "47A60"
    ],
    "keywords": [
      "perturbations",
      "survey article",
      "koplienko-neidhardt trace formulae",
      "schatten-von neumann class",
      "study operator lipschitz"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.1761P"
    }
  }
}