{
  "abstract": "The classical Lebesgue dominated convergence theorem (DCT) is a cornerstone in commutative measure theory, while its extension to the noncommutative setting has remained a longstanding challenge due to the barriers posed by the noncommutative structure. Let \\(α\\) be a unitarily invariant norm defined on a diffuse tracial von Neumann algebra \\((\\mathcal{M}, τ)\\), let $L^α(\\mathcal M, τ)$ be the completion of $\\mathcal M$ with respect to the norm $α$(which includes all $L^p(\\mathcal M, τ)$ as special cases). In this paper, by replacing ``almost everywhere convergence\" with Nelson's convergence in measure, we establish a noncommutative analog of the dominated convergence theorem for $L^α(\\mathcal M, τ)$ under a { significantly weaker dominating condition} than those previously considered. For instance, in a \\(II_1\\) factor \\(\\mathcal{M}\\), if \\(P\\) is a projection with \\(τ(P)=\\frac{1}{n}\\), then \\(n^2 P\\) ``dominates\" every operator of norm \\(\\leq n\\). As an application, we obtain a complete characterization of center-preserving $*$-automorphism of finite von Neumann algebras, which unifies and extends the earlier works of Kadison and Haagerup on the structure of automorphisms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34776",
  "author_total": 4,
  "authors": [
    {
      "name": "Yanni Chen"
    },
    {
      "name": "Don Hadwin"
    },
    {
      "name": "Junhao Shen"
    },
    {
      "name": "Ye Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1b32dhhybkf2w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34776",
  "fulltext_url": null,
  "id": "1b32dhhybkf2w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34776",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7224003283",
  "pdf_url": "https://arxiv.org/pdf/2610.34776",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1b32dhhybkf2w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34776",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34776"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Measure Convergence under Weak Domination for Unitarily Invariant Norms on Finite von Neumann Algebras",
  "title_text": "Measure Convergence under Weak Domination for Unitarily Invariant Norms on Finite von Neumann Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/1b32dhhybkf2w",
  "venue": "arXiv",
  "versions": []
}