{
  "abstract": "We prove that every $p$-absolutely Cesàro bounded operator with constant $K>1$ is $q$-absolutely Cesàro bounded for $1\\leq q<pK/(K-1)$. This range is optimal, even for positive weighted shifts. On Banach spaces of type $s\\in (1,2]$, we prove that every absolutely Cesàro bounded operator is $q$-absolutely Cesàro bounded for every $1\\leq q<s$, with a logarithmic estimate at $q=s$. We also prove the polynomial growth bound $\\| T^n \\| =O(n^{1/s-\\varepsilon})$ for some $\\varepsilon>0$. On $L^p$-spaces, $1<p<\\infty$, we extend the implication from absolute Cesàro boundedness to $p$-absolute Cesàro boundedness from positive to individually eventually positive operators. Finally, for every $1\\leq p<\\infty$, we construct a $p$-absolutely Cesàro bounded operator $T$ on $\\ell^1$ such that $σ(T)\\subseteq\\mathbb D\\cup\\{1\\}$ but $\\limsup_{n\\to\\infty}\\|T^n(I-T)\\|=\\infty$. We also observe that the construction yields a single operator which is $p$-absolutely Cesàro bounded for every $1\\leq p<\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00271",
  "author_total": 1,
  "authors": [
    {
      "name": "Loris Arnold"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c51c5y8ybzmce.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00271",
  "fulltext_url": null,
  "id": "c51c5y8ybzmce",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00271",
  "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.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7215762961",
  "pdf_url": "https://arxiv.org/pdf/2610.00271",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c51c5y8ybzmce.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00271",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00271"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Self-improvement for absolutely Cesáro bounded operators",
  "title_text": "Self-improvement for absolutely Cesáro bounded operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/c51c5y8ybzmce",
  "venue": "arXiv",
  "versions": []
}