{
  "abstract": "We establish finite-dimensional von Neumann type inequalities for commuting matrix tuples in noncommutative operator balls. Let $Ω=\\mathbb{D}_Q$ be the NC operator ball of a linear pencil $Q$ with linearly independent coefficients. If $Ω(1)$ admits a transitive subgroup of automorphisms with NC lifts and $Ω(1)$ has the bounded $H^\\infty$-Gleason property at the origin, then $\\|f(T)\\|\\leq C_{Ω,n}\\|f\\|_{H^\\infty(Ω(1))}$ for every commuting tuple $T\\inΩ(n)$, with $C_{Ω,n}=(2ρ_ΩK_Ω)^{n-1}$; here $K_Ω$ is the Gleason constant and $ρ_Ω$ is the sum of the suprema of the coordinate functions on $Ω(1)$. The scalar coordinate bounds persist at every matrix level. The hypotheses hold for products of row and column balls, where $ρ_Ω=d$, yielding an unconditional estimate $(2dK_Ω)^{n-1}$. For a general type I Cartan domain $R_{p,q}$, we obtain only a conditional result: the same bound holds provided the scalar domain has the bounded $H^\\infty$-Gleason property at the origin, which we do not establish when $\\min(p,q)\\geq 2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20355",
  "author_total": 1,
  "authors": [
    {
      "name": "Ran Kiri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2b079e6z3ycvv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20355",
  "fulltext_url": null,
  "id": "2b079e6z3ycvv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20355",
  "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.CV"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7221929928",
  "pdf_url": "https://arxiv.org/pdf/2610.20355",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2b079e6z3ycvv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20355",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20355"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Von Neumann Type Inequalities for NC Operator Balls",
  "title_text": "Von Neumann Type Inequalities for NC Operator Balls",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/2b079e6z3ycvv",
  "venue": "arXiv",
  "versions": []
}