{
  "abstract": "We establish a quaternionic Hansen--Pedersen inequality for real operator-convex functions on right quaternionic Hilbert spaces. The proof is based on the continuous real functional calculus for selfadjoint quaternionic operators, a direct-sum functional-calculus identity, and a block-unitary construction. As an application, let \\(T = U|T|\\) be an injective \\(p\\)-hyponormal operator. We prove that, for \\(0 < r \\leq 1/2\\), the transform \\(S_{r}(T) = U|T|^{r}U\\) is \\(2p\\)-hyponormal when \\(0 < p \\leq 1/2\\) and hyponormal when \\(1/2 < p \\leq 1\\). We also show that \\(S_{r}(T)\\) preserves log-hyponormality for \\(r > 0\\). These results illustrate the use of quaternionic Jensen-type operator inequalities in the study of transforms associated with the polar decomposition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32623",
  "author_total": 1,
  "authors": [
    {
      "name": "M. Fashandi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6v0zbty1b1h9j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32623",
  "fulltext_url": null,
  "id": "6v0zbty1b1h9j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32623",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.32623",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6v0zbty1b1h9j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32623",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32623"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Quaternionic Hansen--Pedersen Inequality and its Application to $S_r$-Transforms",
  "title_text": "A Quaternionic Hansen--Pedersen Inequality and its Application to S_r-Transforms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/6v0zbty1b1h9j",
  "venue": "arXiv",
  "versions": []
}