{
  "abstract": "This paper extends the Kadison duality between compact convex sets and function systems to the setting of partial convexity. A partially convex set is a set that is convex in a designated set of convex variables when the others are held fixed. We introduce the notion of a regular partially convex set and identify its dual as a finitely generated free module over a commutative C*-algebra endowed with a compatible Archimedean order unit structure. We call such spaces free order unit modules. We prove that for any compact regular partially convex set K, the space of continuous functions on K that are affine in the convex variables is the canonical example of such a module. Conversely, we show that the partially convex state space of a free order unit module is a compact regular partially convex set. Our main result establishes a duality between compact regular partially convex sets and free order unit modules. We also establish a Stone-Weierstrass-type theorem, demonstrating that partially affine polynomials are dense in the space of continuous partially affine functions on any compact regular partially convex set. Finally, we prove a Hahn-Banach-type separation theorem of compact partially convex sets from their outer points.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.03709",
  "author_total": 1,
  "authors": [
    {
      "name": "Tea Štrekelj"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5dxrqa08jzph2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.03709",
  "fulltext_url": null,
  "id": "5dxrqa08jzph2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.03709",
  "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 Operator Algebra Research"
    ]
  ],
  "openalex": "W7160439074",
  "pdf_url": "https://arxiv.org/pdf/2605.03709",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5dxrqa08jzph2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2605.03709",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.03709"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Kadison duality for partially convex sets",
  "title_text": "Kadison duality for partially convex sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/5dxrqa08jzph2",
  "venue": "arXiv",
  "versions": []
}