{"paper":{"title":"Full factors, bicentralizer flow and approximately inner automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.OA","authors_text":"Amine Marrakchi","submitted_at":"2018-11-26T09:52:27Z","abstract_excerpt":"We show that a factor $M$ is full if and only if the $C^*$-algebra generated by its left and right regular representations contains the compact operators. We prove that the bicentralizer flow of a type $\\mathrm{III}_1$ factor is always ergodic. As a consequence, for any type $\\mathrm{III}_1$ factor $M$ and any $\\lambda \\in ]0,1]$, there exists an irreducible AFD type $\\mathrm{III}_\\lambda$ subfactor with expectation in $M$. Moreover, any type $\\mathrm{III}_1$ factor $M$ which satisfies $M \\cong M \\otimes R_\\lambda$ for some $\\lambda \\in ]0,1[$ has trivial bicentralizer. Finally, we give a coun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10253","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"}