{
  "abstract": "We prove a noncommutative maximal ergodic inequality for averages along polynomial sequences. Let $γ$ be a trace-preserving automorphism of a semifinite von Neumann algebra $(\\mathcal N,τ)$. We show that the associated polynomial averages \\begin{equation*} A_Nf:=\\frac1N\\sum_{n=1}^Nγ^{P(n)}(f), \\qquad N\\in\\mathbb N, \\end{equation*} satisfy a strong maximal inequality on $L_p(\\mathcal N)$ for every $1<p<\\infty$, extending the previously known restricted range of $p$. The proof follows Bourgain's major-arc strategy but requires substantially new ideas and tools for operators that may have further applications in noncommutative analysis. More precisely, we obtain a localized maximal inequality by developing a noncommutative version of Stein's extrapolation, novel combinatorial methods, and a surprising multilinear version of Doob's maximal inequality. For the required decaying $L_2$-approximation, we combine two of Bourgain's constructions in a way that avoids the multi-frequency maximal inequality used in the scalar proof.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06455",
  "author_total": 4,
  "authors": [
    {
      "name": "Guixiang Hong"
    },
    {
      "name": "Wenbo Li"
    },
    {
      "name": "Eric Ricard"
    },
    {
      "name": "Liang Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2tz72tqm1daw8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06455",
  "fulltext_url": null,
  "id": "2tz72tqm1daw8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06455",
  "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.CA"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7220723105",
  "pdf_url": "https://arxiv.org/pdf/2610.06455",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2tz72tqm1daw8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06455",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06455"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Noncommutative maximal inequalities for polynomial ergodic averages",
  "title_text": "Noncommutative maximal inequalities for polynomial ergodic averages",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/2tz72tqm1daw8",
  "venue": "arXiv",
  "versions": []
}