{"paper":{"title":"Asymptotic structure of 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, Yoshimichi Ueda","submitted_at":"2015-03-09T12:55:23Z","abstract_excerpt":"Let $(M, \\varphi) = (M_1, \\varphi_1) \\ast (M_2, \\varphi_2)$ be the free product of any $\\sigma$-finite von Neumann algebras endowed with any faithful normal states. We show that whenever $Q \\subset M$ is a von Neumann subalgebra with separable predual such that both $Q$ and $Q \\cap M_1$ are the ranges of faithful normal conditional expectations and such that both the intersection $Q \\cap M_1$ and the central sequence algebra $Q' \\cap M^\\omega$ are diffuse (e.g. $Q$ is amenable), then $Q$ must sit inside $M_1$. This result generalizes the previous results of the first named author in [Ho14] and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02460","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"}