{
  "abstract": "For a positive integer $m$ and a real parameter $α>-1$, consider the generalized Cesàro matrix on $\\ell^2(\\mathbb N_0)$ with entries $m(n-j+1)_{m-1}/(n+α+1)_m$ for $j\\le n$. We give a computer-assisted proof that this operator is hyponormal if and only if $α\\ge0$. The main algebraic ingredient is an explicit decomposition of an auxiliary defect operator into a positive diagonal operator and at most $m$ rank-one operators. Discrete Gram polynomials determine the signs and coefficients of these terms. For nonnegative parameters, weighted estimates reduce positivity to scalar inequalities. A uniform analytic estimate covers every $m\\ge32768$, while finite rational certificates cover the remaining orders and entire parameter intervals, without parameter sampling or truncating an infinite operator. The proof also gives a uniform weighted lower bound for the self-commutator. For $-1<α<0$, finite-support vectors give negative quadratic forms for every order.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00193",
  "author_total": 1,
  "authors": [
    {
      "name": "Yicen Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cp0gnzw6bpejx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00193",
  "fulltext_url": null,
  "id": "cp0gnzw6bpejx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00193",
  "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"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7216139193",
  "pdf_url": "https://arxiv.org/pdf/2610.00193",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cp0gnzw6bpejx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00193",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00193"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Hyponormality of Generalized Cesàro Matrices of Every Positive Integer Order",
  "title_text": "Hyponormality of Generalized Cesàro Matrices of Every Positive Integer Order",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/cp0gnzw6bpejx",
  "venue": "arXiv",
  "versions": []
}