{"paper":{"title":"Amenability of Closed Subgroups and Orlicz Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.RT","authors_text":"Yaroslav Kopylov","submitted_at":"2013-05-29T15:08:17Z","abstract_excerpt":"We prove that a closed subgroup $H$ of a second countable locally compact group $G$ is amenable if and only if its left regular representation on an Orlicz space $L^\\Phi(G)$ for some $\\Delta_2$-regular $N$-function $\\Phi$ almost has invariant vectors. We also show that a noncompact second countable locally compact group $G$ is amenable if and ony if the first cohomology space $H^1(G,L^\\Phi(G))$ is non-Hausdorff for some $\\Delta_2$-regular $N$-function $\\Phi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6828","kind":"arxiv","version":3},"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"}