{
  "abstract": "Let $\\mathcal{H}$ be a separable infinite dimensional Hilbert space and $\\mathcal{B}(\\mathcal{H})$ the algebra of all bounded linear operators on $\\mathcal{H}$. A subalgebra $\\mathfrak{A}$ in $\\mathcal{B}(\\mathcal{H})$ has the left (resp.\\ right) partial factorization property if for any invertible operator $S\\in\\mathcal{B}(\\mathcal{H})$, there exists an isometry (resp.\\ a co-isometry) $U\\in\\mathcal{B}(\\mathcal{H})$ such that $U^*S, S^{-1}U\\in\\mathfrak{A}$. We show that if $\\mathfrak{A}$ is weak operator topology closed with the left (resp.\\ right) partial factorization property, then $\\mathfrak{A}$ is the nest algebra associated with its invariant subspace lattice. In particular, if $\\mathfrak{A}$ is transitive, then $\\mathfrak{A}=\\mathcal{B}(\\mathcal{H})$. This gives a positive answer to Question 6.3 raised by B.V.R. Bhat and M. Kumar in \\emph{Publ. Res. Inst. Math. Sci.} \\textbf{60}(2024), 507--537.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27479",
  "author_total": 2,
  "authors": [
    {
      "name": "Fengyang Jia"
    },
    {
      "name": "Guoxing Ji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4da61y37b19j0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27479",
  "fulltext_url": null,
  "id": "4da61y37b19j0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27479",
  "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": "W7214226132",
  "pdf_url": "https://arxiv.org/pdf/2609.27479",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4da61y37b19j0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27479",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27479"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Partial factorization and reflexivity of operator algebras",
  "title_text": "Partial factorization and reflexivity of operator algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/4da61y37b19j0",
  "venue": "arXiv",
  "versions": []
}