{
  "abstract": "We study whether every infinite-dimensional weakly compactly generated (WCG) Banach space fails the Lotz property. The answer is affirmative in the nonseparable case: a classical decomposition theorem for WCG spaces provides a Schauder decomposition, and an explicit diagonal $C_0$-semigroup has an unbounded generator. The unrestricted assertion is false. Our main abstract result is a Calkin-algebra criterion: if $X$ fails the bounded compact approximation property and, for some fixed $m$, every noninvertible element of $\\Cal(X)=\\Lop(X)/\\Kop(X)$ has $m$th power zero, then $X$ has the Lotz property. In particular, this applies when every operator is scalar-plus-strictly-singular and one fixed power of every strictly singular operator is compact. Combining this criterion with the Maurey--Pisier--Szankowski extraction theorem and constructions of Argyros and Motakis yields separable hereditarily indecomposable Lotz spaces over both scalar fields: reflexive examples, and, over the complex field, an example containing no infinite-dimensional reflexive subspace. Moreover, the ambient Argyros--Motakis spaces considered here are Lotz-saturated, although they themselves are non-Lotz. Thus every nonseparable WCG space is non-Lotz, while the separable WCG class contains both Lotz and non-Lotz spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38396",
  "author_total": 4,
  "authors": [
    {
      "name": "Gustavo Araújo"
    },
    {
      "name": "Mateus Azevedo"
    },
    {
      "name": "Flank Bezerra"
    },
    {
      "name": "Anderson Barbosa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/db9xk0e0q0m6v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38396",
  "fulltext_url": null,
  "id": "db9xk0e0q0m6v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38396",
  "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": "W7215076953",
  "pdf_url": "https://arxiv.org/pdf/2609.38396",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/db9xk0e0q0m6v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38396",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38396"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Lotz Property in Weakly Compactly Generated Spaces",
  "title_text": "The Lotz Property in Weakly Compactly Generated Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/db9xk0e0q0m6v",
  "venue": "arXiv",
  "versions": []
}