{
  "abstract": "We prove that there exists an absolute constant $c>1$ such that for every $n \\geq 3$ there exists an $n$-dimensional real normed space $X$ for which every linear projection $P$ onto a hyperplane satisfies $\\|P\\| \\geq c$. More generally, for every integer $k \\geq 1$ there exists a constant $c_k>1$ such that for every $n \\geq k+2$ there exists an $n$-dimensional real normed space $X$ such that every projection $P$ onto a subspace of codimension at most $k$ satisfies $\\|P\\| \\geq c_k$. The proof is based on an idea of Gleit and Lazar, who established an analogous result for the space of real $n \\times n$ matrices equipped with either the trace-class norm or the operator norm",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09113",
  "author_total": 1,
  "authors": [
    {
      "name": "Tomasz Kobos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7z21n43h9kaej.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09113",
  "fulltext_url": null,
  "id": "7z21n43h9kaej",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09113",
  "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": "W7220930868",
  "pdf_url": "https://arxiv.org/pdf/2610.09113",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7z21n43h9kaej.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09113",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09113"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Finite-dimensional normed spaces without small-norm hyperplane projections",
  "title_text": "Finite-dimensional normed spaces without small-norm hyperplane projections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/7z21n43h9kaej",
  "venue": "arXiv",
  "versions": []
}