{
  "abstract": "For every $n\\in\\mathbb N$, we construct a finite metric subspace $M_n$ of $\\ell_\\infty^n$ such that the Lipschitz-free space $\\mathcal F(M_n)$ contains a linear isometric copy of $\\ell_\\infty^n$. This answers a question posed by Khan, Mim, and Ostrovskii, who obtained examples in dimensions three and four. As a consequence, the finite-dimensional real Banach spaces that admit a linear isometric embedding into a Lipschitz-free space over a finite metric space are precisely the polyhedral spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16230",
  "author_total": 1,
  "authors": [
    {
      "name": "Rainis Haller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/380rd61f5a2ah.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16230",
  "fulltext_url": null,
  "id": "380rd61f5a2ah",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16230",
  "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": "W7213414766",
  "pdf_url": "https://arxiv.org/pdf/2609.16230",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/380rd61f5a2ah.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16230",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16230"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Isometric copies of $\\ell_\\infty^n$ in Lipschitz-free spaces over finite metric spaces",
  "title_text": "Isometric copies of ℓ_∞^n in Lipschitz-free spaces over finite metric spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/380rd61f5a2ah",
  "venue": "arXiv",
  "versions": []
}