{
  "abstract": "Let $A^2(\\mathbb D)$ be the unweighted Bergman space and write $Q_m(S)=T_{B_m(S)}$ for the map induced by the $m$th higher-order Berezin transform. Suárez asked in 2005 whether $Q_m(S)$ converges to $S$ in operator norm for every $S$ in the full Bergman Toeplitz algebra. We answer this question negatively in a strong form: there is a compact operator $S$ such that \\[ \\sup_{m\\geq 0}\\|Q_m(S)\\|=\\infty. \\] In particular, along a strictly increasing sequence $(m_n)$ one has \\[ \\|Q_{m_n}(S)-S\\|\\longrightarrow\\infty. \\] The obstruction is a moving matrix edge. The proof uses a moving family of rank-one test operators, each supported in the $m$th matrix column. Near the corresponding edge, these test operators are sent to weighted Hankel matrices, and the limiting coefficients form an explicit Pascal kernel. We prove a standalone Pascal--Hankel theorem showing that the associated weighted Hankel transformation fails to map $\\ell^2$ boundedly into trace class. Finite-section convergence, trace duality, and the Uniform Boundedness Principle then transfer this instability to the exact Bergman maps.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10846",
  "author_total": 2,
  "authors": [
    {
      "name": "Mishko Mitkovski"
    },
    {
      "name": "Yuyuan Ouyang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/erkb6feeprny4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10846",
  "fulltext_url": null,
  "id": "erkb6feeprny4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10846",
  "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",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7212280860",
  "pdf_url": "https://arxiv.org/pdf/2609.10846",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/erkb6feeprny4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10846",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10846"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Compact Counterexample to Suárez's Berezin Approximation Question",
  "title_text": "A Compact Counterexample to Suárez's Berezin Approximation Question",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/erkb6feeprny4",
  "venue": "arXiv",
  "versions": []
}