{
  "abstract": "We provide a strengthened answer to the questions posed by Alonso, Martín, and Papini [Studia Math. 188 (2008), 135--150] concerning the comparison between the von Neumann--Jordan and James constants . The classical inequality $\\CNJ(X)\\leq J(X)$ between the von Neumann--Jordan and James constants was established by Takahashi and Kato [J. Math. Anal. Appl. 359 (2009), 602--609], Wang [Proc. Amer. Math. Soc. 138 (2010), 695--701], and Yang and Li [Appl. Math. Lett. 23 (2010), 277--281], while related sharp estimates were obtained by Kato and Takahashi [Rend. Circ. Mat. Palermo (2) Suppl. 82 (2010), 75--91]. We sharpen this inequality to $\\CNJ(X)\\leq\\JB(X)$, where $\\JB(X)$ is the Birkhoff--James orthogonal James constant introduced by Baronti and Papini [Constr. Math. Anal. 5 (2022), 37--45]. Our proof employs optimal distance ellipses and alternating contact directions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13360",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhiyao Fang"
    },
    {
      "name": "Qi Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1s910pn7hhvwq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13360",
  "fulltext_url": null,
  "id": "1s910pn7hhvwq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13360",
  "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",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7221572867",
  "pdf_url": "https://arxiv.org/pdf/2610.13360",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1s910pn7hhvwq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.13360",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13360"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "An Improved Inequality between the von Neumann-Jordan and James Constants",
  "title_text": "An Improved Inequality between the von Neumann-Jordan and James Constants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/1s910pn7hhvwq",
  "venue": "arXiv",
  "versions": []
}