{
  "id": "1207.6229",
  "version": "v1",
  "published": "2012-07-26T10:28:25.000Z",
  "updated": "2012-07-26T10:28:25.000Z",
  "title": "Weakly admissible $H^{\\infty}(\\C_{-})$-calculus on general Banach spaces",
  "authors": [
    "Felix Schwenninger",
    "Hans Zwart"
  ],
  "comment": "30 pages, Extension of the article 'F.L. Schwenninger, H.Zwart, Weakly admissible $\\mathcal{H}_{\\infty}^{-}$-calculus on reflexive Banach spaces' to be published in Indagationes Mathematicae (2012), DOI:10.1016/j.indag.2012.04.005. Main additions: Generalization to general Banach spaces and relation to the natural half-plane calculus",
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that, given a Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded) functional calculus. The construction uses a Toeplitz operator and is motivated by system theory. In separable Hilbert spaces, we even get admissibility. Furthermore, it is investigated when a bounded calculus can be guaranteed. For this we introduce the new notion of exact observability by direction. Finally, it is shown that the calculus coincides with one for half-plane-operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-26T10:28:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A60",
      "47D06",
      "47B35",
      "93C25"
    ],
    "keywords": [
      "general banach spaces",
      "calculus coincides",
      "left half-plane",
      "functional calculus",
      "toeplitz operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.6229S"
    }
  }
}