{
  "abstract": "We show that for every $n\\in \\mathbb{N}$, the Lipschitz-free space $\\mathcal{F}(\\mathbb{R}^n)$ has the Dunford-Pettis property. As a consequence, for every $n\\in \\mathbb{N}$ and every nonempty $M\\subset \\mathbb{R}^n$, the space $\\mathcal{F}(M)$ has the Dunford-Pettis property. This implies that $\\mathcal{F}(M)$ is not isomorphic to $\\mathcal{F}(X)$ for any separable Banach space $X$ that fails the Dunford-Pettis property. In particular, this applies to $X=\\ell_2$, and more generally to every infinite-dimensional separable reflexive space. We also deduce that if $1<p<\\infty$, then $\\mathcal{F}(\\ell_p)$ is not isomorphic to $\\left(\\bigoplus\\limits_{n=1}^\\infty \\mathcal{F}(\\ell_p^n) \\right)_{\\ell_1}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28842",
  "author_total": 1,
  "authors": [
    {
      "name": "Fraser Mason"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/998kct00jh727.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28842",
  "fulltext_url": null,
  "id": "998kct00jh727",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28842",
  "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": "W7214369556",
  "pdf_url": "https://arxiv.org/pdf/2609.28842",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/998kct00jh727.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28842",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28842"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Dunford-Pettis property for Lipschitz-free spaces over $\\mathbb{R}^n$",
  "title_text": "The Dunford-Pettis property for Lipschitz-free spaces over ℝ^n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/998kct00jh727",
  "venue": "arXiv",
  "versions": []
}