{
  "abstract": "This paper develops a unified theory of joint $q$-numerical ranges $\\Fq(F)$ for continuous functions $F:\\Om \\to \\B(\\cH)$, where $\\Om$ is a compact Hausdorff space and $\\B(\\cH)$ denotes the $C^*$-algebra of bounded linear operators on a complex Hilbert space $\\cH$. We prove that $\\Fq(F)$ is totally bounded in $\\cC(\\Om)$, the space of continuous complex-valued functions on $\\Om$, and establish the upper semicontinuity of the set-valued map $F\\mapsto \\Fq(F)$, and show that $\\Fq(F)$ is compact when $\\cH$ is finite-dimensional. The main result of the paper is a realization theorem. We prove that, for every totally bounded subset $K$ of $\\cC(\\Om)$ and every $q\\in \\C$ with $|q|=1$, there exist a Hilbert space $\\cH$ and a continuous function $F:\\Om\\to\\B(\\cH)$ such that $qK\\subset \\Fq(F)\\subset q\\cok$. Consequently, if $K$ is closed and convex, then $\\Fq(F)=qK$. As applications, we derive analogous realization results for bounded subsets in $\\C^n$ and for totally bounded subsets in arbitrary Banach spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32504",
  "author_total": 1,
  "authors": [
    {
      "name": "Amin Azadi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bc6d5gywky69j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32504",
  "fulltext_url": null,
  "id": "bc6d5gywky69j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32504",
  "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.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7223664257",
  "pdf_url": "https://arxiv.org/pdf/2610.32504",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bc6d5gywky69j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32504",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32504"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Joint q-Numerical Ranges of Continuous Operator-Valued Functions",
  "title_text": "Joint q-Numerical Ranges of Continuous Operator-Valued Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/bc6d5gywky69j",
  "venue": "arXiv",
  "versions": []
}