{
  "abstract": "Let \\(Ω\\) be a compact Hausdorff space, and let \\(\\cA\\) be a unital \\(C^*\\)-algebra. In this study, we continue our examination of the comparison between \\(C^*\\)-extreme points and linear extremal structures of the unit ball, in the vector-valued \\(C^*\\)-algebra \\(C(Ω, \\cA)\\), building upon the work initiated in \\cite{HR}. We first enlarge the class of $C^\\ast$-algebras in which a $ C^\\ast$-extreme point is an extreme point. We demonstrate that if \\(\\cA\\) has a faithful tracial state, then any \\(C^*\\)-extreme point of the unit ball \\(C(Ω, \\cA)_1\\) is a unitary. Additionally, we identify a classes of \\(C^*\\)-algebras where the concepts of \\(C^*\\)-extreme and pointwise \\(C^*\\)-extreme points in \\(C(Ω, \\cA)_1\\) coincide. We show this holds if a von Neumann algebra has a separable predual with the Radon-Nikodým property.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02680",
  "author_total": 2,
  "authors": [
    {
      "name": "Neha Hotwani"
    },
    {
      "name": "T. S. S. R. K. Rao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8npmj7yzktqby.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02680",
  "fulltext_url": null,
  "id": "8npmj7yzktqby",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02680",
  "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.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7207719648",
  "pdf_url": "https://arxiv.org/pdf/2609.02680",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8npmj7yzktqby.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02680",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02680"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Vector valued continuous function spaces as $C^\\ast$-algebras",
  "title_text": "Vector valued continuous function spaces as C^∗-algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/8npmj7yzktqby",
  "venue": "arXiv",
  "versions": []
}