{
  "id": "1812.11299",
  "version": "v1",
  "published": "2018-12-29T06:47:07.000Z",
  "updated": "2018-12-29T06:47:07.000Z",
  "title": "New counterexamples on Ritt operators, sectorial operators and R-boundedness",
  "authors": [
    "Loris Arnold",
    "Christian Le Merdy"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\mathcal D$ be a Schauder decomposition on some Banach space $X$. We prove that if $\\mathcal D$ is not $R$-Schauder, then there exists a Ritt operator $T\\in B(X)$ which is a multiplier with respect to $\\mathcal D$, such that the set $\\{T^n\\, :\\, n\\geq 0\\}$ is not $R$-bounded. Likewise we prove that there exists a bounded sectorial operator $A$ of type $0$ on $X$ which is a multiplier with respect to $\\mathcal D$, such that the set $\\{e^{-tA}\\, : \\, t\\geq 0\\}$ is not $R$-bounded.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-29T06:47:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A99",
      "46B15"
    ],
    "keywords": [
      "ritt operator",
      "r-boundedness",
      "counterexamples",
      "banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}