{
  "abstract": "We prove a simultaneous Williamson's normal form for two symplectically commuting positive operators $A, B$ on a real symplectic Hilbert space $(\\mathbf{H}, J)$. Under a natural commutativity condition, there exists a (generally unbounded) operator $Φ$ that simultaneously diagonalizes $A$ and $B$ in the symplectic setting as $A = Φ^t M_A Φ$, $B = Φ^t M_B Φ$, and maps $J$ to a canonical symplectic operator. The result generalizes Williamson's normal form to infinite dimensions and yields a complete spectral invariant for the pair $(A,B)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04583",
  "author_total": 2,
  "authors": [
    {
      "name": "Rudra Kamat"
    },
    {
      "name": "Anmary Tonny"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ezdg68pbbz3tg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04583",
  "fulltext_url": null,
  "id": "ezdg68pbbz3tg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04583",
  "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"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
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  ],
  "openalex": "W7220728692",
  "pdf_url": "https://arxiv.org/pdf/2610.04583",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ezdg68pbbz3tg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04583",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04583"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Simultaneous Williamson's normal form for positive operators",
  "title_text": "Simultaneous Williamson's normal form for positive operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/ezdg68pbbz3tg",
  "venue": "arXiv",
  "versions": []
}