{
  "abstract": "For every $0<p<1$, we establish maximal spaceability of the bounded operators on $\\ell_p$ which fail to be $(r,s)$-absolutely summing for all $1\\le s\\le r<\\infty$, using the coordinate-disjointization construction and Maddox's theorem. We give detailed isometric estimates and prove a corresponding maximal spaceability theorem inside the compact operators. The compact result is based on an explicit diagonal multiplier and a single weakly $1$-summable sequence witnessing the simultaneous failure of all admissible absolute summability conditions. A diagonal characterization, a logarithmic compact example, and extensions to operators with values in quasi-Banach spaces containing a copy of $\\ell_p$ are also obtained. The constructed subspaces are isomorphic to $\\ell_p$ and have maximal algebraic dimension whenever the ambient operator spaces have dimension $\\mathfrak c$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33999",
  "author_total": 1,
  "authors": [
    {
      "name": "Daniel Araújo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dkampzjxk54mh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33999",
  "fulltext_url": null,
  "id": "dkampzjxk54mh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33999",
  "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": "W7223829957",
  "pdf_url": "https://arxiv.org/pdf/2610.33999",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dkampzjxk54mh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33999",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33999"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Maximal Spaceability of the set of non-absolutely summing operators in quasi-Banach spaces",
  "title_text": "Maximal Spaceability of the set of non-absolutely summing operators in quasi-Banach spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/dkampzjxk54mh",
  "venue": "arXiv",
  "versions": []
}