{"paper":{"title":"On the multiplication of operator-valued c-free random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jiun-Chau Wang, Mihai Popa, Victor Vinnikov","submitted_at":"2015-09-29T17:07:53Z","abstract_excerpt":"We discuss some results concerning the multiplication of non-commutative random variables that are c-free with respect to a pair $( \\Phi, \\varphi) $, where $ \\Phi $ is a linear map with values in some Banach or C$^\\ast$-algebra and $ \\varphi $ is scalar-valued. In particular, we construct a suitable analogue of the Voiculescu's $ S $-transform for this framework."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08853","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"}