{
  "abstract": "We study Hilbert transforms on graph products of finite von Neumann algebras, with particular interest in their boundedness on the associated noncommutative $L_p$-spaces for $1<p<\\infty$. We establish a generalized Cotlar identity for Hilbert transforms, valid on operators whose lengths exceed a constant depending only on the underlying graph. We further prove that graph products of finite von Neumann algebras satisfying a Haagerup-type inequality admit $L_p$-bounded Hilbert transforms, therefore extending the corresponding result of Mei and Ricard for free products of finite von Neumann algebras. In addition, we obtain several equivalent characterizations of this Haagerup-type inequality. Our results apply, in particular, to graph products of finite groups, right-angled Hecke von Neumann algebras, and graph products of finite quantum groups. As an application, we provide a complete characterization of a compactness problem posed by Ozawa for graph products of finite groups and right-angled Hecke von Neumann algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.00194",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiao-Qi Lu"
    },
    {
      "name": "Runlian Xia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f8g6s9056fjp9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.00194",
  "fulltext_url": null,
  "id": "f8g6s9056fjp9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.00194",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7167058544",
  "pdf_url": "https://arxiv.org/pdf/2607.00194",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f8g6s9056fjp9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2607.00194",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.00194"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Hilbert transforms on graph products of finite von Neumann algebras",
  "title_text": "Hilbert transforms on graph products of finite von Neumann algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/f8g6s9056fjp9",
  "venue": "arXiv",
  "versions": []
}