{
  "id": "2505.05788",
  "version": "v1",
  "published": "2025-05-09T05:11:34.000Z",
  "updated": "2025-05-09T05:11:34.000Z",
  "title": "$H^\\infty$ Functional Calculus for a Commuting tuple of $\\text{Ritt}_{\\text{E}}$ Operators",
  "authors": [
    "Suman Mondal",
    "Subhajit Palai",
    "Samya Kumar Ray"
  ],
  "comment": "25 pages, 1 figure",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this article, we develop a framework for the joint functional calculus of commuting tuples of $\\text{Ritt}_{\\text{E}}$ operators on Banach spaces. We establish a transfer principle that relates the bounded holomorphic functional calculus for tuples of $\\text{Ritt}_{\\text{E}}$ operators to that of their associated sectorial counterparts. In addition, we prove a joint dilation theorem for commuting tuples of $\\text{Ritt}_{\\text{E}}$ operators on a broad class of Banach spaces. As a key application, we obtain an equivalent set of criteria on $L^p$-spaces for $1<p< \\infty$ that determine when a commuting tuple of $\\text{Ritt}_{\\text{E}}$ operators admits a joint bounded functional calculus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-09T05:11:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "commuting tuple",
      "banach spaces",
      "joint bounded functional calculus",
      "joint functional calculus",
      "bounded holomorphic functional calculus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}