{"paper":{"title":"Gamma stability in free product von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Cyril Houdayer","submitted_at":"2014-03-17T14:00:43Z","abstract_excerpt":"Let $(M, \\varphi) = (M_1, \\varphi_1) \\ast (M_2, \\varphi_2)$ be a free product of arbitrary von Neumann algebras endowed with faithful normal states. Assume that the centralizer $M_1^{\\varphi_1}$ is diffuse. We first show that any intermediate subalgebra $M_1 \\subset Q \\subset M$ which has nontrivial central sequences in $M$ is necessarily equal to $M_1$. Then we obtain a general structural result for all the intermediate subalgebras $M_1 \\subset Q \\subset M$ with expectation. We deduce that any diffuse amenable von Neumann algebra can be concretely realized as a maximal amenable subalgebra wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4098","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"}