{
  "id": "2403.01574",
  "version": "v1",
  "published": "2024-03-03T17:43:23.000Z",
  "updated": "2024-03-03T17:43:23.000Z",
  "title": "On $\\mathfrak{L}_{\\infty}$-liftings of the Gelfand-Naimark morphism",
  "authors": [
    "Vasily Melnikov"
  ],
  "journal": "Matematicheskie Zametki 115 (2024) 925-929",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Let $M$ be a $W^{\\ast}$-algebra acting on a separable complex Hilbert space $H$. We show that the inclusion of $M$ into $\\mathscr{B}(H)$ factors through an $\\mathfrak{L}_{\\infty}$-space only if $M$ is a finite type $\\mathrm{I}$ algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-03T17:43:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46L10"
    ],
    "keywords": [
      "gelfand-naimark morphism",
      "separable complex hilbert space",
      "finite type"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}