{"paper":{"title":"Asymptotic orthogonalization of subalgebras in II$_1$ factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Sorin Popa","submitted_at":"2017-07-23T15:57:26Z","abstract_excerpt":"Let $M$ be a II$_1$ factor with a von Neumann subalgebra $Q\\subset M$ that has infinite index under any projection in $Q'\\cap M$ (e.g., $Q$ abelian; or $Q$ an irreducible subfactor with infinite Jones index). We prove that given any separable subalgebra $B$ of the ultrapower II$_1$ factor $M^\\omega$, for a non-principal ultrafilter $\\omega$ on $\\Bbb N$, there exists a unitary element $u\\in M^\\omega$ such that $uBu^*$ is orthogonal to $Q^\\omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07317","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"}