{
  "abstract": "We introduce and study $\\mathcal{FG}$-order continuous operators between Riesz spaces, based on Tantrawan's generalized (unbounded) order convergence. This framework includes several familiar classes of operators and allows their properties to be studied in a unified setting. We establish order boundedness and lattice-theoretic results; in particular, we show that strongly order continuous operators are automatically order bounded and prove that the modulus of an order bounded $\\mathcal{FG}$-order continuous operator remains $\\mathcal{FG}$-order continuous under suitable assumptions. The latter result gives an affirmative answer to a previously posed problem for strongly order continuous operators. We also establish a general result ensuring classical order continuity, from which order continuity results for several familiar classes of operators follow. Furthermore, we characterize, under suitable hypotheses, when the space of order bounded $\\mathcal{FG}$-order continuous operators is a band. Finally, we prove an extension theorem for positive $\\mathcal{FG}$-order continuous operators, providing a counterpart of Veksler's extension theorem in this framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23893",
  "author_total": 1,
  "authors": [
    {
      "name": "Ayse Uyar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4p92b5zwvwkm3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23893",
  "fulltext_url": null,
  "id": "4p92b5zwvwkm3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23893",
  "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.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7214052900",
  "pdf_url": "https://arxiv.org/pdf/2609.23893",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4p92b5zwvwkm3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23893",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23893"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A General Framework for Operator Continuity between Riesz Spaces",
  "title_text": "A General Framework for Operator Continuity between Riesz Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/4p92b5zwvwkm3",
  "venue": "arXiv",
  "versions": []
}