{
  "abstract": "Building on the results of \\cite{HR}, we investigate the relationship between \\(C^*\\)-extremality and linear extremality in the closed unit balls of general unital \\(C^*\\)-algebras. We show that, unlike in von Neumann algebras, these two notions of extremality need not coincide in general \\(C^*\\)-algebras. More precisely, we prove that the unilateral shift is a linear extreme point, but not a \\(C^*\\)-extreme point, of the closed unit ball of the Toeplitz \\(C^*\\)-algebra. We further establish that \\(C^*\\)-extremality implies linear extremality whenever the \\(C^*\\)-algebra admits a faithful unital representation on a separable Hilbert space. We also prove this implication for elements admitting a factorization $x=v|x|$, where $v$ is a partial isometry belonging to the algebra, and extend the result to suitable quotient \\(C^*\\)-algebras, including the Calkin algebra. Finally, we characterize the linear extreme points of the closed unit ball of unital \\(C^*\\)-subalgebras of \\(B(H)\\) containing the compact operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03563",
  "author_total": 1,
  "authors": [
    {
      "name": "Neha Hotwani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2sh9kzr1q4yd3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03563",
  "fulltext_url": null,
  "id": "2sh9kzr1q4yd3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03563",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03563",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2sh9kzr1q4yd3.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03563",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03563"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Geometric Aspects of $C^*$-Extreme Points II",
  "title_text": "Geometric Aspects of C^*-Extreme Points II",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/2sh9kzr1q4yd3",
  "venue": "arXiv",
  "versions": []
}