{
  "abstract": "We introduce the class $LW_+$ of $L$-tauberian operators and its dual counterpart, the class $MW_-$ of $M$-cotauberian operators. We obtain sequential, perturbative, and algebraic characterizations of these classes. As a consequence, every $T\\in LW_+(E,Y)$ is disjointly non-singular, and the converse implication holds if and only if every dispersed subspace of $E$ has equi-integrable unit ball. For $E=L_p$, the latter property depends on $p$. For $1\\leq p<2$, equi-integrability of the unit ball is equivalent to dispersedness, and $L$-tauberian operators coincide with disjointly non-singular operators, while for $p\\geq 2$ these equivalences fail. Moreover, $LW_+(L_p)$ is neither open nor stable under composition. Applying a result of Haydon, Odell, and Schlumprecht, we show that for $2<p<\\infty$ every infinite dimensional dispersed subspace of $L_p$ contains an infinite dimensional subspace with equi-integrable unit ball. However, we give an example showing that this is not true for $p=2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32432",
  "author_total": 2,
  "authors": [
    {
      "name": "Alberto Caldera"
    },
    {
      "name": "Manuel González"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9amhqtf7ynz8h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32432",
  "fulltext_url": null,
  "id": "9amhqtf7ynz8h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32432",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7223699478",
  "pdf_url": "https://arxiv.org/pdf/2610.32432",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9amhqtf7ynz8h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32432",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32432"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$L$-tauberian operators and subspaces with equi-integrable unit ball",
  "title_text": "L-tauberian operators and subspaces with equi-integrable unit ball",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/9amhqtf7ynz8h",
  "venue": "arXiv",
  "versions": []
}