{
  "abstract": "We prove that equivalent locally compact, locally Hausdorff, étale groupoids with paracompact unit spaces have Morita equivalent reduced and full $L^p$-operator algebras for every $p\\in[1,\\infty]$. The reduced theorem requires pairing-valued approximate identities, reflecting the failure of unconditionality of the reduced norm for $1<p<\\infty$, while the full theorem rests on a full-clopen reduction theorem proved by dilating spatial representations. For $1\\leq p<\\infty$, we also compare the concrete $p$-linking algebra of the reduced Morita equivalence with the reduced $L^p$-operator algebra of the linking groupoid: the canonical comparison is contractive, injective, and has dense range in general, and is an isometric isomorphism for $p=2$. We further study Morita cycles arising from proper étale groupoid correspondences, including the reduced case under suitable extension hypotheses. Applications include an $L^p$ version of Green's symmetric imprimitivity theorem, results for coarse groupoids and inverse semigroups, and invariance of the corresponding $K$-theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39031",
  "author_total": 3,
  "authors": [
    {
      "name": "Yeong Chyuan Chung"
    },
    {
      "name": "Alonso Delfín"
    },
    {
      "name": "Zhen Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0w57t42e0hfna.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39031",
  "fulltext_url": null,
  "id": "0w57t42e0hfna",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39031",
  "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.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7215125838",
  "pdf_url": "https://arxiv.org/pdf/2609.39031",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0w57t42e0hfna.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39031",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39031"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Morita equivalence for $L^p$-operator algebras associated with étale groupoids",
  "title_text": "Morita equivalence for L^p-operator algebras associated with étale groupoids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/0w57t42e0hfna",
  "venue": "arXiv",
  "versions": []
}