{
  "abstract": "We show that the norm-closed linear span of products of two Dunford-Pettis operators on $L^1(0,1)$ lies strictly between the representable and the Dunford-Pettis operators. This gives an additional proper large closed ideal in $\\mathcal{B}(L^1(0,1))$, answering the existence question of Johnson, Pisier and Schechtman. The quotient of the Dunford-Pettis ideal by this square ideal contains a contractively complemented isometric copy of $L^1(0,1)$. We also prove that the Dunford-Pettis ideal has no right approximate identity, answering a question of Johnson and Schechtman. More precisely, a positive norm-one convolution operator $R$ satisfies $\\|R-RT\\|\\geq1$ and $\\|R-TR\\|\\geq1$ for every Dunford-Pettis operator $T$. The proofs combine translation averaging, Rajchman measures supported on a strongly independent set, and two atomless disintegrations of positive operators. The approximate-identity obstruction extends to every finite measure space with a nonzero atomless part. Finally, we prove that quantitative multiplication estimates for an ideal pass to all its closed power ideals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18348",
  "author_total": 1,
  "authors": [
    {
      "name": "Amir Bahman Nasseri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ddc3srn195k9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18348",
  "fulltext_url": null,
  "id": "6ddc3srn195k9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18348",
  "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": "W7213530860",
  "pdf_url": "https://arxiv.org/pdf/2609.18348",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ddc3srn195k9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18348",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18348"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Large ideals in B(L1(0,1))",
  "title_text": "Large ideals in B(L1(0,1))",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/6ddc3srn195k9",
  "venue": "arXiv",
  "versions": []
}