{"paper":{"title":"Ideal structure of $\\ell^p$ uniform Roe algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Xinhui Du, Yeong Chyuan Chung","submitted_at":"2026-06-10T02:27:27Z","abstract_excerpt":"For a uniformly locally finite coarse space $(X,\\mathcal{E})$, we prove that for every $p\\in\\{0\\}\\cup[1,\\infty]$, the lattice of geometric ideals in the $\\ell^p$ uniform Roe algebra $B^p_u(X,\\mathcal{E})$ is isomorphic to the lattice of ideals of $\\mathcal{E}$ (equivalently, to the lattice of ideals in the associated family of controlled partial coverings of $X$). In particular, the lattices of geometric ideals for different values of $p$ coincide. Using limit operators, we establish a canonical isometric isomorphism between $B^p_u(X,\\mathcal{E})$ and the reduced $L^p$ operator algebra of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11586","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11586/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}