{
  "abstract": "In 1970, P. R. Halmos raised ten open problems on operator theory. The third problem of Halmos is the following: if an intransitive operator has an inverse, is its inverse also intransitive? This question is reduced to the case of conjugate bi-geometric operators in arXiv: 2610.11202. In the framework of conjugate bi-geometric operators, using tools from complex geometry, operator theory, and function theory, this paper gives an affirmative answer to the third problem of Halmos in the following cases: (a) bundle-preserving operator;(b) subexponential growth of operator norms. These two cases cover a large class of operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12857",
  "author_total": 3,
  "authors": [
    {
      "name": "Kui Ji"
    },
    {
      "name": "Chunlan Jiang"
    },
    {
      "name": "Zhenyue Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3jjrhv23y84ca.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12857",
  "fulltext_url": null,
  "id": "3jjrhv23y84ca",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12857",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7221546350",
  "pdf_url": "https://arxiv.org/pdf/2610.12857",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3jjrhv23y84ca.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.12857",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12857"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Geometric operators and the third problem of Halmos",
  "title_text": "Geometric operators and the third problem of Halmos",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/3jjrhv23y84ca",
  "venue": "arXiv",
  "versions": []
}