{
  "id": "0805.0209",
  "version": "v1",
  "published": "2008-05-02T11:08:09.000Z",
  "updated": "2008-05-02T11:08:09.000Z",
  "title": "Application of topological radicals to calculation of joint spectral radii",
  "authors": [
    "Victor S. Shulman",
    "Yuri V. Turovskii"
  ],
  "categories": [
    "math.FA",
    "math.SP"
  ],
  "abstract": "It is shown that the joint spectral radius $\\rho(M)$ of a precompact family $M$ of operators on a Banach space $X$ is equal to the maximum of two numbers: the joint spectral radius $\\rho_{e}(M)$ of the image of $M$ in the Calkin algebra and the Berger-Wang radius $r(M)$ defined by the formula \\[ r(M)=\\underset{n\\to\\infty}{\\limsup}(\\sup\\left\\{\\rho(a):a\\in M^{n}\\right\\} ^{1/n}) . \\] Some more general Banach-algebraic results of this kind are also proved. The proofs are based on the study of special radicals on the class of Banach algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-02T11:08:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D03",
      "46H05"
    ],
    "keywords": [
      "joint spectral radius",
      "topological radicals",
      "application",
      "calculation",
      "general banach-algebraic results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.0209S"
    }
  }
}