{
  "abstract": "We show that the natural tensor product multiplication of two Archimedean almost \\(f\\)-algebras does not, in general, extend to their Fremlin tensor product. The two algebras in the counterexample have the same underlying vector lattice \\(C[0,1]\\). Their multiplications are explicit, positive and nilpotent of index three. The obstruction is the fact that the function \\((s,t)\\mapsto e^{st}\\) does not belong to \\(C[0,1]\\ftensor C[0,1]\\). The same construction gives Banach almost \\(f\\)-algebras and has consequences for previously published assertions on Riesz and Fremlin projective tensor products of almost \\(f\\)-algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33963",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohamed Amine Ben Amor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/84z2eza8y6md2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33963",
  "fulltext_url": null,
  "id": "84z2eza8y6md2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33963",
  "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": "W7214732808",
  "pdf_url": "https://arxiv.org/pdf/2609.33963",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/84z2eza8y6md2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33963",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33963"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Tensor Products of Almost \\(f\\)-Algebras: A Counterexample",
  "title_text": "Tensor Products of Almost f-Algebras: A Counterexample",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/84z2eza8y6md2",
  "venue": "arXiv",
  "versions": []
}