{
  "id": "1411.1815",
  "version": "v1",
  "published": "2014-11-07T03:20:33.000Z",
  "updated": "2014-11-07T03:20:33.000Z",
  "title": "Functions of perturbed noncommuting self-adjoint operators",
  "authors": [
    "Aleksei Aleksandrov",
    "Fedor Nazarov",
    "Vladimir Peller"
  ],
  "comment": "6 pages",
  "categories": [
    "math.FA",
    "math.CA",
    "math.CV",
    "math.SP"
  ],
  "abstract": "We consider functions $f(A,B)$ of noncommuting self-adjoint operators $A$ and $B$ that can be defined in terms of double operator integrals. We prove that if $f$ belongs to the Besov class $B_{\\be,1}^1(\\R^2)$, then we have the following Lipschitz type estimate in the trace norm: $\\|f(A_1,B_1)-f(A_2,B_2)\\|_{\\bS_1}\\le\\const(\\|A_1-A_2\\|_{\\bS_1}+\\|B_1-B_2\\|_{\\bS_1})$. However, the condition $f\\in B_{\\be,1}^1(\\R^2)$ does not imply the Lipschitz type estimate in the operator norm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-07T03:20:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A60",
      "47A55"
    ],
    "keywords": [
      "perturbed noncommuting self-adjoint operators",
      "lipschitz type estimate",
      "operator norm",
      "besov class",
      "trace norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.1815A"
    }
  }
}