{
  "abstract": "In this paper, we consider the strong operator topology (SOT) on the space $\\mathcal{L} (X)$ of continuous linear operators on an infinite-dimensional Fréchet space $X$. The existence of SOT-dense subspaces as well as of SOT-closed infinite-dimensional subspaces inside the family of all non-cyclic operators is established. Other classes of operators, such as non-dense range or non-injective operators, are also studied in this regard. Moreover, we prove for the sequence space $\\ell_p$ $(0 < p < \\infty)$ that the family of all non-cyclic members of $\\mathcal{L}(\\ell_p)$ contains an isometric copy of $\\ell_p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27211",
  "author_total": 5,
  "authors": [
    {
      "name": "N. G. Albuquerque"
    },
    {
      "name": "G. Araújo"
    },
    {
      "name": "L. Bernal-González"
    },
    {
      "name": "E. Demétrio Jr."
    },
    {
      "name": "J. Seoane-Sepúlveda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1vep5rhtbc0w5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27211",
  "fulltext_url": null,
  "id": "1vep5rhtbc0w5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27211",
  "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": "W7214243255",
  "pdf_url": "https://arxiv.org/pdf/2609.27211",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1vep5rhtbc0w5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27211",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27211"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "SOT-large subspaces of non-cyclic operators",
  "title_text": "SOT-large subspaces of non-cyclic operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/1vep5rhtbc0w5",
  "venue": "arXiv",
  "versions": []
}