{
  "abstract": "We prove that every subspace $V\\subset\\ell_\\infty^N$ of codimension one or two with absolute projection constant $λ(V)<4/3$ satisfies $$ d(V,\\ell_\\infty^{\\dim V}) \\leq\\frac{λ(V)}{4-3λ(V)}. $$ We conjecture that the codimension assumption can be removed and that the same estimate holds for every subspace $V\\subset\\ell_\\infty^N$ with $λ(V)<4/3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06141",
  "author_total": 2,
  "authors": [
    {
      "name": "Beata Deregowska"
    },
    {
      "name": "Barbara Lewandowska"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/55y7rerpzds6g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06141",
  "fulltext_url": null,
  "id": "55y7rerpzds6g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06141",
  "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": "W7220679521",
  "pdf_url": "https://arxiv.org/pdf/2610.06141",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/55y7rerpzds6g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06141",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06141"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Projection Constants and Banach-Mazur Distance in Codimension Two",
  "title_text": "Projection Constants and Banach-Mazur Distance in Codimension Two",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/55y7rerpzds6g",
  "venue": "arXiv",
  "versions": []
}