{
  "abstract": "This paper provides a complex-analytic interpretation of certain topologies on the tensor algebra, which are a central tool within strict deformation quantization. We prove that the symmetric tensor algebra $\\operatorname{S}(V)$ of a barelled nuclear DF-space $V$ endowed with any of these topologies may be understood as an algebra of bounded Fréchet holomorphic functions on the strong dual space $V'_β$. The coarsest of the topologies then corresponds to the topology of uniform convergence on bounded subsets. The finer ones provide an infinite-dimensional generalization of the order of an entire holomorphic function. To facilitate these results, we study the interplay between boundedness and continuity of holomorphic mappings between locally convex spaces. As a byproduct, we establish a simple sufficient criterion for Fréchet holomorphy as well as several completeness results for spaces of bounded functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16250",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael Heins"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c1zq1emkppvx2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16250",
  "fulltext_url": null,
  "id": "c1zq1emkppvx2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16250",
  "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-ph"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.FA"
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      "arxiv",
      "math.MP"
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      "arxiv",
      "math.QA"
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      "openalex",
      "2610|Advanced Banach Space Theory"
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  "openalex": "W7213405102",
  "pdf_url": "https://arxiv.org/pdf/2609.16250",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c1zq1emkppvx2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.16250",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16250"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Boundedness in Strict Deformation Quantization",
  "title_text": "Boundedness in Strict Deformation Quantization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/c1zq1emkppvx2",
  "venue": "arXiv",
  "versions": []
}