{"paper":{"title":"An approximation theorem for nuclear operator systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Kyung Hoon Han, Vern I. Paulsen","submitted_at":"2010-09-14T00:11:37Z","abstract_excerpt":"We prove that an operator system $\\mathcal S$ is nuclear in the category of operator systems if and only if there exist nets of unital completely positive maps $\\phi_\\lambda : \\cl S \\to M_{n_\\lambda}$ and $\\psi_\\lambda : M_{n_\\lambda} \\to \\cl S$ such that $\\psi_\\lambda \\circ \\phi_\\lambda$ converges to ${\\rm id}_{\\cl S}$ in the point-norm topology. Our proof is independent of the Choi-Effros-Kirchberg characterization of nuclear $C^*$-algebras and yields this characterization as a corollary. We give an example of a nuclear operator system that is not completely order isomorphic to a unital $C^*"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2541","kind":"arxiv","version":4},"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"}