{"paper":{"title":"A property (T) for C*-algebras","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Bachir Bekka","submitted_at":"2005-05-10T17:35:10Z","abstract_excerpt":"We define a notion of Property (T) for an arbitrary $C^*$-algebra $A$ admitting a tracial state. We extend this to a notion of Property (T) for the pair $(A,B),$ where $B$ is a $C^*$-subalgebra of $A.$ Let $\\Gamma$ be a discrete group and $C^*_r(\\Gamma)$ its reduced algebra. We show that $C^*_r(\\Gamma)$ has Property (T) if and only if the group $\\Gamma$ has Property (T) . More generally, given a subgroup $\\Lambda$ of $\\Gamma$, the pair $(C^*_r(\\Gamma),C^*_r(\\Lambda))$ has Property (T) if and only if the pair of groups $(\\Gamma, \\Lambda)$ has Property (T)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505189","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":""},"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"}