{
  "abstract": "Problem 8.4 of Pino, Goodearl, Perera and Molina in [arxiv.org/abs/0806.4156] asks whether a dense subalgebra $A_{0}$ of a $C^*$-algebra $A$ that is purely infinite as a ring forces $A$ to be purely infinite as a $C^*$-algebra. We call this the $\\textit{pure infiniteness transfer problem}$, the transfer being from the ring to its $C^*$-completion. The problem is open, even when $A_{0}$ is unital and simple. We settle it under two hypotheses: $A$ has real rank zero, and $A_{0}$ is closed under holomorphic functional calculus. Under these hypotheses $A_{0}$ is purely infinite simple as a ring if and only if $A$ is purely infinite simple as a $C^*$-algebra. We also prove an obstruction: a unital $C^*$-algebra with a nonzero finite projection has no dense hfc-closed purely infinite simple unital subring. Finally, the hypotheses hold for proper subalgebras, for the gauge action of $\\mathbb{T}$ on a Cuntz algebra $\\mathcal{O}_n$ , the smooth subalgebra $\\mathcal{O}_n^\\infty$ is a proper dense hfc-closed subalgebra that is purely infinite simple as a ring.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30906",
  "author_total": 1,
  "authors": [
    {
      "name": "Arindam Sutradhar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c9eg8xkhnx6w5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30906",
  "fulltext_url": null,
  "id": "c9eg8xkhnx6w5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30906",
  "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": "W7204970993",
  "pdf_url": "https://arxiv.org/pdf/2608.30906",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c9eg8xkhnx6w5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2608.30906",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30906"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The pure infiniteness transfer problem",
  "title_text": "The pure infiniteness transfer problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/c9eg8xkhnx6w5",
  "venue": "arXiv",
  "versions": []
}