Operator space and operator system analogs of Kirchberg's nuclear embedding theorem

The Gurarij operator space NGNG 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 φ:X→NGφ:X→NG and a completely contractive projection from NGNG onto the range of φ  . This can be seen as the operator space analog of Kirchberg's nuclear embedding theorem. With similar methods we also establish the natural operator system analog of Kirchberg's nuclear embedding theorem involving the Gurarij operator system GSGS.