{
  "abstract": "Let $\\mathfrak{c}=2^{\\aleph_0}$. We prove that $\\ell_\\infty$ contains $2^{\\mathfrak{c}}$ pairwise non-isomorphic non-reflexive Grothendieck subspaces. They may all be chosen to contain the canonical copy of $c_0$ and to have infinite-dimensional reflexive quotient. This is optimal and answers by the authors in 2021. We also show that the relative $\\ell_\\infty$-Grothendieck property depends on the specified copy of $c_0$ and is not an isomorphic invariant of the subspace. More generally, for every closed $E\\subseteq\\ell_\\infty$ there is an $\\ell_\\infty$-Grothendieck subspace isomorphic to $\\ell_\\infty\\oplus_\\infty E$; taking $E=c_0$ answers a problem by González et al.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20170",
  "author_total": 2,
  "authors": [
    {
      "name": "Manuel González"
    },
    {
      "name": "Tomasz Kania"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/deej5j0d4511b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20170",
  "fulltext_url": null,
  "id": "deej5j0d4511b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20170",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7213597230",
  "pdf_url": "https://arxiv.org/pdf/2609.20170",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/deej5j0d4511b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20170",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20170"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Grothendieck and $\\ell_\\infty$-Grothendieck subspaces of $\\ell_\\infty$",
  "title_text": "Grothendieck and ℓ_∞-Grothendieck subspaces of ℓ_∞",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/deej5j0d4511b",
  "venue": "arXiv",
  "versions": []
}