{
  "id": "1310.4672",
  "version": "v2",
  "published": "2013-10-17T12:20:32.000Z",
  "updated": "2014-10-07T09:52:30.000Z",
  "title": "On the structure of semigroups on $L_p$ with a bounded $H{^\\infty}$-calculus",
  "authors": [
    "Stephan Fackler"
  ],
  "comment": "14 pages; final version",
  "journal": "Bull. Lond. Math. Soc. 46 (2014), no. 5, 1063-1076",
  "doi": "10.1112/blms/bdu062",
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that a bounded analytic semigroup on an $L_p$-space has a bounded $H^{\\infty}(\\Sigma_{\\varphi})$-calculus for some $\\varphi < \\frac{\\pi}{2}$ if and only if the semigroup can be obtained, after restricting to invariant subspaces, factorizing through invariant subspaces and similarity transforms, from a bounded analytic semigroup on some bigger $L_p$-space which is positive and contractive on the real line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-17T12:20:32.000Z",
      "comment": "13 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-07T09:52:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A60",
      "47D06",
      "46L07",
      "47L25"
    ],
    "keywords": [
      "bounded analytic semigroup",
      "invariant subspaces",
      "real line",
      "similarity transforms"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4672F"
    }
  }
}