{
  "abstract": "Let $A$ and $B$ be $C^*$-algebras, not necessarily unital, and let $T:A_+\\to B_+$ be a positively homogeneous order isomorphism. We first prove that $T$ is additive and extends uniquely to a bounded real-linear order isomorphism between the self-adjoint parts of $A$ and $B$. Passing to the biduals, we then obtain a representation theorem for positively homogeneous order isomorphisms. Finally, we study surjective maps between the positive cones of $C^*$-algebras, again not necessarily unital, which preserve the norm of the arithmetic mean. This extends a previous result by removing the assumption that at least one of the algebras is unital.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21339",
  "author_total": 2,
  "authors": [
    {
      "name": "Osamu Hatori"
    },
    {
      "name": "Shiho Oi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/818wyrj2qwsvt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21339",
  "fulltext_url": null,
  "id": "818wyrj2qwsvt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21339",
  "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 Operator Algebra Research"
    ]
  ],
  "openalex": "W7213914562",
  "pdf_url": "https://arxiv.org/pdf/2609.21339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/818wyrj2qwsvt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21339"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Order isomorphisms on positive cones of non-unital $C^*$-algebras",
  "title_text": "Order isomorphisms on positive cones of non-unital C^*-algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/818wyrj2qwsvt",
  "venue": "arXiv",
  "versions": []
}