{
  "abstract": "We determine the Serre closure of Banach spaces in the category of quasi-Banach spaces, that is, the smallest class of quasi-Banach spaces that contains all Banach spaces and is stable under subspaces, quotients, and extensions. Precisely, a quasi-Banach space $X$ belongs to this closure if and only if there exist constants $M$ and $k\\in\\mathbb N$ such that $$ \\frac{\\|x_1+\\dots+x_n\\|}{\\|x_1\\|+\\dots+\\|x_n\\|}\\leq M\\log^k n $$ for every $n\\geq 2$ and every $x_1,\\dots,x_n\\in X$; equivalently, $X$ is a quotient of an Orlicz sequence space $\\ell(I,f_l)$, where $I$ is an index set and $f_l(t)$ is equivalent to $t\\log^l(1/t)$ near zero. The proof combines geometrical estimates for quasi-Banach spaces and quasilinear maps with the study of higher order derived spaces associated to complex interpolation between $\\ell_{2/3}$ and $\\ell_2$. We provide examples of spaces in the Serre closure of Banach spaces that are not iterated extensions of Banach spaces and discuss some related problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35259",
  "author_total": 4,
  "authors": [
    {
      "name": "Félix Cabello Sánchez"
    },
    {
      "name": "Jesús M. F. Castillo"
    },
    {
      "name": "Raúl Martínez-Bohórquez"
    },
    {
      "name": "José Navarro Garmendia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5q8w6jk6r17q0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35259",
  "fulltext_url": null,
  "id": "5q8w6jk6r17q0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35259",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7223878357",
  "pdf_url": "https://arxiv.org/pdf/2610.35259",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5q8w6jk6r17q0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35259",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35259"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Serre closure of Banach spaces",
  "title_text": "The Serre closure of Banach spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/5q8w6jk6r17q0",
  "venue": "arXiv",
  "versions": []
}