{
  "abstract": "We study Toeplitz operators acting on radial weighted Fock spaces. We use tools from representation theory to construct commutative families of $C^*$-algebras that are generated by Toeplitz operators whose symbols are invariant under the action of $\\U(n)$. For a partition $m=(b_1,...,b_k)$ of an integer $n$, we realize \\[\\mathbf{\\U_m}:=\\U(b_1)\\times...\\times\\U(b_k)\\] as a block diagonally subgroup of $\\U(n)$ and describe the decomposition of the weighted Fock space into irreducible $\\mathbf{U_m}$-modules. This allows us to study Toeplitz operators with $\\mathbf{U_m}$-invariant, equivalently $k$-quasi-radial, symbols. Also, we provide an explicit integral representation of their eigenvalues. More generally, for an arbitrary compact subgroup $H\\subseteq\\U(n)$, we characterize the commutativity of the $C^*$-algebra generated by $H$-invariant Toeplitz operators in terms of the multiplicity-free property of the representation $π|_H$. Finally, for a logarithmically growing radial weight, we construct a bounded radial symbol for which the corresponding eigenvalue sequence is not uniformly continuous with respect to the square-root metric. Consequently, the uniform closure of the set of eigenvalue sequences does not coincide with the $C^*$-algebra of bounded sequences that are uniformly continuous with respect to the square-root metric.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20652",
  "author_total": 1,
  "authors": [
    {
      "name": "Khalid Bdarneh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/12fxzjjtj74dr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20652",
  "fulltext_url": null,
  "id": "12fxzjjtj74dr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20652",
  "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.OA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7213603659",
  "pdf_url": "https://arxiv.org/pdf/2609.20652",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/12fxzjjtj74dr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.20652",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20652"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Toeplitz $C^*$-algebras on radially weighted Fock spaces: commutativity and spectral representation",
  "title_text": "Toeplitz C^*-algebras on radially weighted Fock spaces: commutativity and spectral representation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/12fxzjjtj74dr",
  "venue": "arXiv",
  "versions": []
}