{
  "abstract": "We solve a problem posed by Hu and Virtanen by characterizing, for every $0<p<\\infty$, the bounded symbols $f$ for which $T_f^{(t)}T_g^{(t)}-T_{fg}^{(t)}$ tends to zero in the unnormalized Schatten $p$-norm or quasi-norm as $t\\to0^+$ for every fixed bounded $g$. The setting is weighted Fock spaces over $\\mathbb C^n$ with weights whose real Hessians are uniformly positive and bounded. Only constants satisfy the limit when $p<2n$; at $p=2n$, it is equivalent to the weak real gradient belonging to $L^{2n}(\\mathbb R^{2n})$. When $p>2n$, the limit is characterized by relative weak compactness in $L^1(\\mathbb R^{2n})$ of normalized local mean oscillation densities. For $p\\ge2$, uniform convergence over $\\|g\\|_\\infty\\le1$ is equivalent to vanishing density mass. A continuous compactly supported counterexample for $p>2n$ shows that bounded density mass and convergence for $g=\\bar f$ do not imply convergence for every fixed bounded $g$. The symbol classes are weight-independent unital algebras, yielding limits for finite Toeplitz products and commutators; quantitative Hölder estimates also give finite-rank approximation bounds. The Gaussian case transfers to anti-Wick quantization by unitary equivalence. On compact Kähler manifolds with positive line bundles, we prove a Hölder sufficient condition, including the endpoint, for each fixed bounded second symbol. A projective-line example shows that trace norm convergence can fail for a smooth first symbol and a fixed bounded second symbol. The proofs combine local holomorphic approximation, Schatten and Sobolev estimates, singular integral methods, and the Dunford--Pettis criterion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30787",
  "author_total": 1,
  "authors": [
    {
      "name": "Jie Qin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3j2xf92qfcb15.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30787",
  "fulltext_url": null,
  "id": "3j2xf92qfcb15",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30787",
  "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": "W7223276611",
  "pdf_url": "https://arxiv.org/pdf/2610.30787",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3j2xf92qfcb15.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30787",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30787"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Schatten limits for semi-commutators in Toeplitz quantization on Fock space",
  "title_text": "Schatten limits for semi-commutators in Toeplitz quantization on Fock space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/3j2xf92qfcb15",
  "venue": "arXiv",
  "versions": []
}