{
  "abstract": "This paper introduces and systematically investigates several classes of numerical ranges associated with real-linear operators on Hilbert spaces, including the essential numerical range, maximal numerical range, essential maximal numerical range, $q$-numerical range, and trace numerical range. We establish fundamental structural properties of these sets and characterize their geometric shape. In particular, we analyze how the real-linear nature of the operators influences the geometry and spectral behaviour of the corresponding numerical ranges, thereby extending and enriching the theory of numerical ranges from complex-linear to real-linear operator settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16823",
  "author_total": 2,
  "authors": [
    {
      "name": "Arup Majumdar"
    },
    {
      "name": "Vladimir Muller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5x8a1k0r7f8wa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16823",
  "fulltext_url": null,
  "id": "5x8a1k0r7f8wa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16823",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
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      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7221785872",
  "pdf_url": "https://arxiv.org/pdf/2610.16823",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5x8a1k0r7f8wa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:16Z",
      "native_id": "2610.16823",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16823"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Some Generalized Numerical Ranges of Real-linear Operators on Hilbert Spaces",
  "title_text": "Some Generalized Numerical Ranges of Real-linear Operators on Hilbert Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:16Z",
  "url": "https://research.draconitic.com/paper/5x8a1k0r7f8wa",
  "venue": "arXiv",
  "versions": []
}