{
  "abstract": "Given a unital inclusion of $C^*$-algebras $\\mathcal C \\subset \\mathcal A$ and a unital inclusion $\\mathcal C \\subset \\mathcal B$ into a von Neumann algebra $\\mathcal B$, we investigate the extreme points of unital completely positive maps from $\\mathcal A$ to $\\mathcal B$ that fix $\\mathcal C$ denoted by $UCP_\\mathcal C(\\mathcal A, \\mathcal B)$. This space is obviously convex and $C^*$-convex with respect to the $C^*$-algebra $\\mathcal C' \\cap \\mathcal B$. In this article we show that the $\\mathcal C' \\cap \\mathcal B$-extreme points are exactly the $*$-homomorphisms that fix $\\mathcal C$ when $\\mathcal A$ is commutative and $\\mathcal B$ has a normal faithful center valued trace. This generalizes a result due to Farenick and Morenz where $\\mathcal C = \\mathbb C 1$ and $\\mathcal B = M_n(\\mathbb C)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22685",
  "author_total": 3,
  "authors": [
    {
      "name": "Dimitrios Giannakis"
    },
    {
      "name": "Michael Montgomery"
    },
    {
      "name": "Travis Russell"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1b80mr7ypbdne.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22685",
  "fulltext_url": null,
  "id": "1b80mr7ypbdne",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22685",
  "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.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214014307",
  "pdf_url": "https://arxiv.org/pdf/2609.22685",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1b80mr7ypbdne.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22685",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22685"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$C^*$-extreme maps and $*$-homomorphisms from $C(X)$ to finite von Neumann algebras",
  "title_text": "C^*-extreme maps and *-homomorphisms from C(X) to finite von Neumann algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/1b80mr7ypbdne",
  "venue": "arXiv",
  "versions": []
}