{
  "abstract": "Motivated by the weak maximizing property ($\\mathrm{WMP}$), we investigate $p$-summability conditions on maximizing sequences of bounded linear operators. Since the naive $p$-summability formulation is independent of $p$ and collapses to norm attainment for all operators, we introduce the weakly $p$-singular maximizing property ($\\mathrm{SMP}_p$), based on maximizing sequences with no weakly $p$-summable subsequence. We completely characterize when the pairs $(\\ell_p,\\ell_q)$ and $(\\ell_p,c_0)$ have the $\\mathrm{SMP}_r$, revealing sharp contrasts with the $\\mathrm{WMP}$. We also characterize the Schur property of order $p$ via the $\\mathrm{WMP}$ and the $\\mathrm{SMP}_r$. Under relative weak $p$-precompactness and suitable Dunford-Pettis-type assumptions, we characterize universal norm attainment for operators from $X$ to $Y$ in terms of either the $\\mathrm{SMP}_q$ for adjoint operators or the weak$^{*}$-to-weak$^{*}$ maximizing property, and derive corresponding duality consequences for the $\\mathrm{SMP}_p$. Finally, we introduce $p$-convergent perturbation properties for operators and their adjoints, characterize them for classical sequence spaces, and show that the $p$-convergent perturbation property is strictly weaker than the $\\mathrm{SMP}_p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03988",
  "author_total": 2,
  "authors": [
    {
      "name": "Oscar Iván Blanco Ardila"
    },
    {
      "name": "Vinícius C. C. Miranda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/59xbhszjmvy91.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03988",
  "fulltext_url": null,
  "id": "59xbhszjmvy91",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03988",
  "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": "W7208720418",
  "pdf_url": "https://arxiv.org/pdf/2609.03988",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/59xbhszjmvy91.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03988",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03988"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A $p$-summability approach to the weak maximizing property",
  "title_text": "A p-summability approach to the weak maximizing property",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/59xbhszjmvy91",
  "venue": "arXiv",
  "versions": []
}