{
  "abstract": "We complete the construction of tracial spectral nonassociative $\\mathrm{L}^p$-spaces for general $\\mathrm{JBW}^*$-algebras. More precisely, if $\\mathcal{M}$ is a $\\mathrm{JBW}^*$-algebra equipped with a normal finite faithful trace $τ$ and $1 \\leq p < \\infty$, we prove that $\\|x\\|_{\\mathrm{L}^p(\\mathcal{M})} \\overset{\\mathrm{def}}{=} (τ[(x^* \\circ x)^{\\frac p2}])^{\\frac1p}$, where $x \\in \\mathcal{M}$, defines a norm on $\\mathcal{M}$. This resolves the remaining exceptional case left open by the corresponding result for $\\mathrm{JW}^*$-algebras. The main difficulty is the complexified Albert algebra $\\mathrm{H}_3(\\mathbb{O}_{\\mathbb{C}})$, which admits no embedding into an associative operator algebra. To treat this case, we establish a Jordan analogue of the joint convexity of the Kiefer map $\\mathrm{M}_n \\times \\mathrm{H}_n^{++} \\to \\mathrm{H}_n^{+}$, $(a,h) \\mapsto a^*h^{-1}a$, where $\\mathrm{H}_n$ is the space of Hermitian matrices, and a Jordan version of a variational formula of Carlen and Lieb. This provides a complex Banach space framework for Jordan-algebraic models arising in some generalized probabilistic theories.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.14231",
  "author_total": 1,
  "authors": [
    {
      "name": "Cédric Arhancet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4e9j7fa246a9m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.14231",
  "fulltext_url": null,
  "id": "4e9j7fa246a9m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.14231",
  "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"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7203648812",
  "pdf_url": "https://arxiv.org/pdf/2608.14231",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4e9j7fa246a9m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2608.14231",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.14231"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Spectral nonassociative $\\mathrm{L}^p$-spaces for $\\mathrm{JBW}^*$-algebras",
  "title_text": "Spectral nonassociative L^p-spaces for JBW^*-algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/4e9j7fa246a9m",
  "venue": "arXiv",
  "versions": []
}