{
  "abstract": "In this paper, we prove a sufficient condition for the uniform ball-covering property of closed operator subspaces invariant under selected truncations. We use uniform convexity of the range space and near-contractive finite-rank projection approximations to obtain quantitative coverings with finite-rank centres whenever the truncated images are separable. A weak-star version gives the same covering parameters for quotients by arbitrary weak-star closed subspaces. In the completely bounded setting, the covering parameters are independent of the matrix level. In particular, the duals of all closed subspaces of $S_1(\\ell_2)$ admit coverings with centre norm $2$ and radius $1+\\varepsilon$, for $0<\\varepsilon<1$, at every matrix level. Applications include operator-valued Schur multipliers and, for $1<p<\\infty$, prescribed-support Fourier multipliers on countable amenable groups and finitely generated free groups. The Fourier coverings have finite-support centres in the given operator or completely bounded norms. An endpoint example shows failure of the ball-covering property at $p=1,\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.12538",
  "author_total": 2,
  "authors": [
    {
      "name": "Rui Liu"
    },
    {
      "name": "Jie Shen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/68bs8t19dzyw2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.12538",
  "fulltext_url": null,
  "id": "68bs8t19dzyw2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.12538",
  "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": "W7168413005",
  "pdf_url": "https://arxiv.org/pdf/2607.12538",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/68bs8t19dzyw2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2607.12538",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.12538"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$π$-Properties, Uniformly Convexity and Uniform Ball Coverings Properties",
  "title_text": "π-Properties, Uniformly Convexity and Uniform Ball Coverings Properties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/68bs8t19dzyw2",
  "venue": "arXiv",
  "versions": []
}