{"paper":{"title":"Operator space and operator system analogs of Kirchberg's nuclear embedding theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.OA","authors_text":"Martino Lupini","submitted_at":"2015-02-20T18:36:53Z","abstract_excerpt":"The Gurarij operator space $\\mathbb{NG}$ introduced by Oikhberg is the unique separable $1$-exact operator space that is approximately injective in the category of $1$-exact operator spaces and completely isometric linear maps. We prove that a separable operator space $X$ is nuclear if and only if there exist a linear complete isometry $\\varphi :X\\rightarrow \\mathbb{NG}$ and a completely contractive projection from $\\mathbb{NG}$ onto the range of $\\varphi $. This can be seen as the operator space analog of Kirchberg's nuclear embedding theorem. We also establish the natural operator system ana"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05966","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"}