{"paper":{"title":"Noncommutative Ergodic Theorems for Connected Amenable Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Mu Sun","submitted_at":"2016-05-11T19:04:01Z","abstract_excerpt":"This paper is devoted to the study of noncommutative ergodic theorems for connected amenable locally compact groups. For a dynamical system $(\\mathcal{M},\\tau,G,\\sigma)$, where $(\\mathcal{M},\\tau)$ is a von Neumann algebra with a normal faithful finite trace and $(G,\\sigma)$ is a connected amenable locally compact group with a well defined representation on $\\mathcal{M}$, we try to find the largest noncommutative function spaces constructed from $\\mathcal{M}$ on which the individual ergodic theorems hold. By using the Emerson-Greenleaf's structure theorem, we transfer the key question to provi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03568","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"}