{"paper":{"title":"On some $p$-approximation properties of exact discrete groups and $\\ell^p$ uniform Roe algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Yeong Chyuan Chung","submitted_at":"2026-06-25T16:17:02Z","abstract_excerpt":"We study $p$-approximation properties of $\\ell^p$ uniform Roe algebras and their connections to coarse geometry and group theory. For a discrete metric space $X$ with bounded geometry, we prove that property A implies $p$-nuclearity of the $\\ell^p$ uniform Roe algebra $B^p_u(X)$ for every $p\\in(1,\\infty)$, while $B^1_u(X)$ is always 1-nuclear. We introduce the $p$-invariant translation approximation property ($p$-ITAP) for discrete groups, generalizing the 2-ITAP of Roe. We also introduce the $p$-operator ITAP. For exact groups, we show that the $p$-operator ITAP is equivalent to the $p$-appro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27230","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/2606.27230/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"}