{
  "abstract": "Let $K$ be an uncountable compact metrizable space, and $E$ be a separable Banach space with the uniform primary factorisation property (UPFP) and containing no isomorphic copy of $c_0$. We prove that $C(K, E)$ also has the UPFP. As a consequence, we obtain the primariness of the bi-parameter spaces $C([0,1],\\ell_p)$ and $C([0,1], L_p)$ for $1 \\leq p<\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18993",
  "author_total": 2,
  "authors": [
    {
      "name": "Antonio Acuaviva"
    },
    {
      "name": "Pablo Acuaviva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/58q6j1bqq8tme.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18993",
  "fulltext_url": null,
  "id": "58q6j1bqq8tme",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18993",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7213527381",
  "pdf_url": "https://arxiv.org/pdf/2609.18993",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58q6j1bqq8tme.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18993",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18993"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Uniform Primary Factorisation Property for $C(K,E)$",
  "title_text": "The Uniform Primary Factorisation Property for C(K,E)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/58q6j1bqq8tme",
  "venue": "arXiv",
  "versions": []
}