{
  "abstract": "We establish three new characterisations of coarse embeddability into Hilbert space for discrete metric spaces of bounded geometry in terms of escaping quasi-local couplings, Schur multipliers, and operator norm state localisation. As applications, we prove that if a sparse metric space of bounded geometry is coarsely embeddable into Hilbert space, then every ghost projection in the quasi-local algebra is compact, while we also provide a counterexample to the converse implication. Finally, we characterise coarse embeddability into Hilbert space via the relative Haagerup property for the quasi-local algebra, and investigate its relation to coarse embeddability into $\\ell^p$ for $p>2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21632",
  "author_total": 3,
  "authors": [
    {
      "name": "Kang Li"
    },
    {
      "name": "Jiawen Zhang"
    },
    {
      "name": "Jingming Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/91r34dxpz18kh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21632",
  "fulltext_url": null,
  "id": "91r34dxpz18kh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21632",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7222485430",
  "pdf_url": "https://arxiv.org/pdf/2610.21632",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/91r34dxpz18kh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.21632",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21632"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Characterisations for coarse embeddability via quasi-locality and Schur multipliers",
  "title_text": "Characterisations for coarse embeddability via quasi-locality and Schur multipliers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/91r34dxpz18kh",
  "venue": "arXiv",
  "versions": []
}