{"paper":{"title":"Ergodic Theorems for coset spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.PR"],"primary_cat":"math.DS","authors_text":"Alexander Fish, Michael Bj\\\"orklund","submitted_at":"2014-08-28T12:11:08Z","abstract_excerpt":"We study in this paper the validity of the mean ergodic theorem along \\emph{left} F\\o lner sequences in a countable amenable group $G$. Although the \\emph{weak} ergodic theorem always holds along \\emph{any} left F\\o lner sequence in $G$, we provide examples where the \\emph{mean} ergodic theorem fails in quite dramatic ways. On the other hand, if $G$ does not admit any ICC quotients, e.g. if $G$ is virtually nilpotent, then we prove that the mean ergodic theorem does indeed hold along \\emph{any} left F\\o lner sequence.\n  In the case when a unitary representation of a countable amenable group is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6692","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"}