{
  "abstract": "We prove that every compact operator $T$ on a separable infinite-dimensional complex Hilbert space is a commutator of two compact operators, thereby answering a question of Pearcy and Topping. Moreover, the compact factors $A$ and $B$ can be chosen such that $[A, B] = T$ and $\\max\\{\\Vert{}A\\Vert{},\\Vert{}B\\Vert{}\\}\\leq c\\Vert{}T\\Vert{}^{1/2}$ for a universal constant $c$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20672",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhichao Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5g59tbndr0jrb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20672",
  "fulltext_url": null,
  "id": "5g59tbndr0jrb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20672",
  "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.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7213582586",
  "pdf_url": "https://arxiv.org/pdf/2609.20672",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5g59tbndr0jrb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.20672",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20672"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Every compact operator is a commutator of compact operators",
  "title_text": "Every compact operator is a commutator of compact operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/5g59tbndr0jrb",
  "venue": "arXiv",
  "versions": []
}