{"paper":{"title":"Local rigidity for actions of Kazhdan groups on non commutative $L_p$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Bachir Bekka","submitted_at":"2015-02-03T19:29:49Z","abstract_excerpt":"Given a discrete group $\\Gamma$, a finite factor $\\mathcal N$ and a real number $p\\in [1, +\\infty)$ with $p\\neq 2,$ we are concerned with the rigidity of actions of $\\Gamma$ by linear isometries on the $L_p$-spaces $L_p(\\mathcal N)$ associated to $\\mathcal N$. More precisely, we show that, when $\\Gamma$ and $\\mathcal N$ have both Property (T) and under some natural ergodicity condition, such an action $\\pi$ is locally rigid in the group $G$ of linear isometries of $L_p(\\mathcal N)$, that is, every sufficiently small perturbation of $\\pi$ is conjugate to $\\pi$ under $G$. As a consequence, when "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00970","kind":"arxiv","version":2},"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"}