{"paper":{"title":"Kadison-Kastler stable factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Alan D. Wiggins, Allan M. Sinclair, Erik Christensen, Jan Cameron, Roger R. Smith, Stuart White","submitted_at":"2012-09-18T22:49:34Z","abstract_excerpt":"A conjecture of Kadison and Kastler from 1972 asks whether sufficiently close operator algebras in a natural uniform sense must be small unitary perturbations of one another. For $n\\geq 3$ and a free ergodic probability measure preserving action of $SL_n(\\mathbb Z)$ on a standard nonatomic probability space $(X,\\mu)$, write $M=((L^\\infty(X,\\mu)\\rtimes SL_n(\\mathbb Z))\\,\\overline{\\otimes}\\, R$, where $R$ is the hyperfinite II$_1$ factor. We show that whenever $M$ is represented as a von Neumann algebra on some Hilbert space $\\mathcal H$ and $N\\subseteq\\mathcal B(\\mathcal H)$ is sufficiently clo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4116","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"}