{
  "abstract": "Let $(\\mathcal{M},τ)$ be a tracial von Neumann algebra, $T:L_1(\\mathcal{M},τ)\\to L_1(\\mathcal{M},τ)$ be induced by a normal $τ$-preserving $*$-automorphism of $\\mathcal{M}$, and $x\\in L_1(\\mathcal{M},τ)$. We will prove the bilaterally almost uniform convergence of averages of the form $$\\frac{1}{n}\\sum_{k=0}^{n-1}T^k(x_k),$$ generalizing an ergodic theorem proven by Breiman in \\cite{Breiman57}, where $(x_k)_{k=0}^{\\infty}$ is an element of the noncommutative vector-valued $L_p$-space $L_p(\\mathcal{M},τ;\\ell_\\infty)$ such that there exists $x\\in L_p(\\mathcal{M},τ)$ with $(x_k-x)_{k=0}^{\\infty}\\in L_p(\\mathcal{M},τ;c_0)$. A generalization to semifinite $(\\mathcal{M},τ)$ and general positive Dunford-Schwartz operators $T\\in DS^+(\\mathcal{M},τ)$ is shown as well when $1<p<\\infty$. In addition to these, we also prove a number of generalizations of the results to weighted, subsequential, and other types of averages.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02535",
  "author_total": 1,
  "authors": [
    {
      "name": "Morgan O'Brien"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9cep6t4yakt5y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02535",
  "fulltext_url": null,
  "id": "9cep6t4yakt5y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02535",
  "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.DS"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02535",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9cep6t4yakt5y.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02535",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02535"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Noncommutative extensions of an ergodic theorem of Breiman",
  "title_text": "Noncommutative extensions of an ergodic theorem of Breiman",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/9cep6t4yakt5y",
  "venue": "arXiv",
  "versions": []
}