{"paper":{"title":"Ergodic properties of Bogoliubov automorphisms in free probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.OA","authors_text":"Farrukh Mukhamedov, Francesco Fidaleo","submitted_at":"2009-05-19T05:43:51Z","abstract_excerpt":"We show that some $C^*$--dynamical systems obtained by \"quantizing\" classical ones on the free Fock space, enjoy very strong ergodic properties. Namely, if the classical dynamical system $(X, T, \\m)$ is ergodic but not weakly mixing, then the resulting quantized system $(\\gg,\\a)$ is uniquely ergodic (w.r.t the fixed point algebra) but not uniquely weak mixing. The same happens if we quantize a classical system $(X, T, \\m)$ which is weakly mixing but not mixing. In this case, the quantized system is uniquely weak mixing but not uniquely mixing. Finally, a quantized system arising from a classic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3026","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"}