{
  "abstract": "We show that for any positive operator monotone function $f$ the inequality $\\int_{[0,\\infty)} f(t) \\, \\mathrm{d} \\left\\lVert E^{Δ_{φ,ψ}}(t) ξ_ψ\\right\\rVert^2 + f'_\\infty φ(1-s(ψ)) \\geq \\frac{f(1)}{2} \\Bigl( φ(1) + ψ(1) - \\lVert φ- ψ\\rVert \\Bigr)$ holds, where $φ, ψ\\in \\mathcal{M}_{*,+}$ are two normal positive linear functionals on a von Neumann algebra $\\mathcal{M}$, and $Δ_{φ,ψ}$ is the associated relative modular operator. Choosing $f(t) = t^s$ with $s \\in [0,1]$, the Powers-Størmer-Ogata inequality is recovered.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16184",
  "author_total": 1,
  "authors": [
    {
      "name": "Markus B. Fröb"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/64kr2gw3yqgtw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16184",
  "fulltext_url": null,
  "id": "64kr2gw3yqgtw",
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  "landing_url": "https://arxiv.org/abs/2609.16184",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
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  "openalex": "W7213393313",
  "pdf_url": "https://arxiv.org/pdf/2609.16184",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/64kr2gw3yqgtw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.16184",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16184"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "A generalization of the Powers-Størmer-Ogata inequality",
  "title_text": "A generalization of the Powers-Størmer-Ogata inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/64kr2gw3yqgtw",
  "venue": "arXiv",
  "versions": []
}