{
  "abstract": "We prove a uniform spectral-gap estimate at every even exponent for isometric representations on arbitrary closed subspaces of real $L_p$-spaces. As an application, this result, combined with the work of Bader, Furman, Gelander and Monod, gives an affirmative answer to their Question 4.1: Kazhdan's property $(T)$ implies property $(T_X)$ whenever $X$ is a closed subspace or a quotient of a real $L_p$-space, for every $1<p<\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01447",
  "author_total": 1,
  "authors": [
    {
      "name": "Qingjin Cheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fenry7fxp188j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01447",
  "fulltext_url": null,
  "id": "fenry7fxp188j",
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  "landing_url": "https://arxiv.org/abs/2609.01447",
  "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"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7206209616",
  "pdf_url": "https://arxiv.org/pdf/2609.01447",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fenry7fxp188j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01447",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01447"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Kazhdan's Property $(T)$ for Subspaces and Quotients of $L_p$-Spaces",
  "title_text": "Kazhdan's Property (T) for Subspaces and Quotients of L_p-Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/fenry7fxp188j",
  "venue": "arXiv",
  "versions": []
}