{
  "abstract": "In this paper, we study modulated $(C,α)$-ergodic averages with operator-valued weights and their subsequential versions in the setting of semifinite von Neumann algebras. Our framework combines $(C,α)$-type modulation with operator-valued weights and extends both scalar-weighted and operator-valued weighted ergodic theories. We establish mean ergodic theorems and maximal inequalities for these averages on noncommutative $L_p$-spaces. We then study bilateral almost uniform and almost uniform convergence in noncommutative Orlicz spaces, including convergence along subsequences of density one. A key ingredient in our approach is the introduction of the $p$-convexity condition on the underlying Orlicz function. This condition enables us to transfer appropriate maximal estimates from noncommutative $L_p$-spaces to establish bilateral uniform equicontinuity in measure at zero on the corresponding noncommutative $p$-convex Orlicz spaces. Together with the noncommutative Banach principle, this yields the desired pointwise convergence results. As an additional consequence of our $p$-convexity argument, we extend Rota's theorem to a larger class of noncommutative Orlicz spaces associated with the $p$-convex Orlicz functions considered in this article.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23616",
  "author_total": 3,
  "authors": [
    {
      "name": "Arup Chattopadhyay"
    },
    {
      "name": "Debabrata De"
    },
    {
      "name": "Disha Shaw"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2zey1yw1qs7z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23616",
  "fulltext_url": null,
  "id": "b2zey1yw1qs7z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23616",
  "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": "W7214020250",
  "pdf_url": "https://arxiv.org/pdf/2609.23616",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2zey1yw1qs7z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23616",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23616"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Noncommutative Maximal Ergodic Theorems for Modulated $(C,α)$-Averages with Operator-Valued Weights",
  "title_text": "Noncommutative Maximal Ergodic Theorems for Modulated (C,α)-Averages with Operator-Valued Weights",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/b2zey1yw1qs7z",
  "venue": "arXiv",
  "versions": []
}