{
  "abstract": "Let $1<p<\\infty$ and let $T$ be a positive strongly Kreiss bounded operator on an $L^p$-space. We prove that there exist constants $C,κ>0$ such that \\[ \\|T^N\\| \\leq C \\left( \\log(N+1) \\right)^κ, \\qquad N \\geq 1. \\] This answers a question raised by Arnold and Cuny concerning positive strongly Kreiss bounded operators on $L^p$-spaces. It also shows that the polynomial exponent appearing in the corresponding problem of Deng, Lorist and Veraar has infimum zero. The proof is elementary: positivity yields a local $\\ell^p$-estimate for the orbit on intervals of length of order $\\sqrt N$; a positive vector-valued lifting of $T$ then produces a self-improving estimate which can be iterated down to the logarithmic scale.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27771",
  "author_total": 1,
  "authors": [
    {
      "name": "Loris Arnold"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bqepj706vp0eg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27771",
  "fulltext_url": null,
  "id": "bqepj706vp0eg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27771",
  "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": "W7214160315",
  "pdf_url": "https://arxiv.org/pdf/2609.27771",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bqepj706vp0eg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27771",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27771"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Positive strongly Kreiss bounded operators on $L^p$-spaces have logarithmic power growth",
  "title_text": "Positive strongly Kreiss bounded operators on L^p-spaces have logarithmic power growth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/bqepj706vp0eg",
  "venue": "arXiv",
  "versions": []
}