{
  "abstract": "For either real or complex scalars, we improve the known upper bound for the Banach--Mazur distance between $L_\\infty[0,1]$ and $\\ell_\\infty$, proving $d_{\\operatorname{BM}}(L_\\infty[0,1],\\ell_\\infty)\\leqslant (2+\\sqrt5)^2=9+4\\sqrt5=17.944\\ldots$. The additional input is a stabilised kernel estimate: the copy of $\\ell_\\infty$ in $L_\\infty$ is chosen so that its kernel is an $\\ell_\\infty$-sum of singular two-point hyperplanes, and Cohen's bound-two construction is then applied coordinatewise. The quantitative part of the proof is an asymmetric Pełczyński-type factorisation, with the elementary optimisation included below.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14121",
  "author_total": 1,
  "authors": [
    {
      "name": "Tomasz Kania"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3h0cfzsj305xr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14121",
  "fulltext_url": null,
  "id": "3h0cfzsj305xr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14121",
  "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": "W7221790105",
  "pdf_url": "https://arxiv.org/pdf/2610.14121",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3h0cfzsj305xr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14121",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14121"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Not too many miles from $\\ell_\\infty$ to $L_\\infty$",
  "title_text": "Not too many miles from ℓ_∞ to L_∞",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/3h0cfzsj305xr",
  "venue": "arXiv",
  "versions": []
}