{
  "abstract": "We study $p$-absolutely Cesàro bounded operators, with particular emphasis on self-improvement, weighted shifts, and linear dynamics. Our first main result shows that, for $1<p<\\infty$, every positive absolutely Cesàro bounded operator on $L^p(Ω)$ is automatically $p$-absolutely Cesàro bounded. We then characterize $q$-absolute Cesàro boundedness of backward shifts on weighted $\\ell^p$-spaces for $q\\geq p$ and use this characterization to construct examples exhibiting a wide range of possible growth rates of the powers. In the dynamical direction, we obtain new obstructions to absolute and strong Cesàro boundedness; in particular, no strongly Cesàro bounded operator on a nonzero Banach space is chaotic or upper frequently hypercyclic. We also introduce Cesàro ratio-boundedness and compare it with absolute Cesàro boundedness. Finally, a general Baire-category principle yields a genericity theorem for the failure of $p$-absolute Cesàro boundedness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24601",
  "author_total": 3,
  "authors": [
    {
      "name": "Arafat Abbar"
    },
    {
      "name": "Loris Arnold"
    },
    {
      "name": "Clément Coine"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eqya577czmpkz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24601",
  "fulltext_url": null,
  "id": "eqya577czmpkz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24601",
  "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"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7213996395",
  "pdf_url": "https://arxiv.org/pdf/2609.24601",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eqya577czmpkz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24601",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24601"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On absolutely Cesàro bounded operators",
  "title_text": "On absolutely Cesàro bounded operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/eqya577czmpkz",
  "venue": "arXiv",
  "versions": []
}