{"paper":{"title":"Decomposability of bimodule maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Christian Le Merdy, Lina Oliveira","submitted_at":"2014-04-04T07:55:24Z","abstract_excerpt":"Consider a unital C*-algebra A, a von Neumann algebra M, a unital sub-C*-algebra C of A and a unital *-homomorphism $\\pi$ from C to M. Let u: A --> M be a decomposable map (i.e. a linear combination of completely positive maps) which is a C-bimodule map with respect to $\\pi$. We show that u is a linear combination of C-bimodule completely positive maps if and only if there exists a projection e in the commutant of $\\pi(C)$ such that u is valued in eMe and $e\\pi(.)e$ has a completely positive extension A --> eMe."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1173","kind":"arxiv","version":1},"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"}