{
  "id": "2407.17109",
  "version": "v1",
  "published": "2024-07-24T09:12:36.000Z",
  "updated": "2024-07-24T09:12:36.000Z",
  "title": "Decoupling for Schatten class operators in the setting of Quantum Harmonic Analysis",
  "authors": [
    "Helge Jørgen Samuelsen"
  ],
  "comment": "13 pages",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "We introduce the notion of decoupling for operators, and prove an equivalence between classical $\\ell^qL^p$ decoupling for functions and $\\ell^q\\mathcal{S}^p$ decoupling for operators on bounded sets in $\\mathbb{R}^{2d}$. We also show that the equivalence only depends on the bounded set $\\Omega$, and not the values of $p,q$ nor the partition of $\\Omega$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-24T09:12:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B10",
      "42B15",
      "47G30",
      "47B10"
    ],
    "keywords": [
      "schatten class operators",
      "quantum harmonic analysis",
      "decoupling",
      "bounded set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}