{
  "abstract": "Let $0<p<q\\leq 1$. We show that the Schur $p$-property provides a powerful structural principle for Lipschitz-free $p$-spaces. Our main result asserts that $\\mathcal{F}_p(M)$ has the Schur $p$-property for every $q$-metric space $M$; when $M$ is compact, it has the strong Schur $p$-property, with a constant depending only on $p$ and $q$. As consequences, $\\mathcal{F}_p(M)$ is $\\ell_p$-saturated, contains no isomorphic copy of an infinite-dimensional $r$-Banach space for $p<r\\leq 1$, and every bounded operator from a $p$-Banach space into $\\mathcal{F}_p(M)$ is either compact or fixes a copy of $\\ell_p$. These results settle Questions 6.1, 6.2, 6.5, and 6.6 from our recent work [F. Albiac, J. L. Ansorena, J. B\\'ıma and M. Cúth, Lipschitz free p-spaces for $0<p<1$ in the light of the Schur $p$-property and the compact reduction, J. Geom. Anal. 36 (2026), Paper No. 54] on the Schur $p$-property, together with several related problems. They also confirm a prediction of Kalton and the first-named author from 2009: no infinite-dimensional $q$-Banach space has the $p$-Lipschitz lifting property. Further applications reveal a sharp contrast between the linear and Lipschitz structures of nonlocally convex spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10747",
  "author_total": 3,
  "authors": [
    {
      "name": "Fernando Albiac"
    },
    {
      "name": "José L. Ansorena"
    },
    {
      "name": "Marek Cúth"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/61wqxfrzw68cn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10747",
  "fulltext_url": null,
  "id": "61wqxfrzw68cn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10747",
  "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": "W7212325686",
  "pdf_url": "https://arxiv.org/pdf/2609.10747",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/61wqxfrzw68cn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10747",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10747"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Structural consequences of the Schur $p$-property for Lipschitz-free $p$-spaces",
  "title_text": "Structural consequences of the Schur p-property for Lipschitz-free p-spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/61wqxfrzw68cn",
  "venue": "arXiv",
  "versions": []
}