Nuclearity related properties in operator systems

Abstract

We investigate the stability of nuclearity related properties in the category of operator systems. In the finite dimensional case, exactness and the lifting property are shown to be dual pairs. Moreover, the lifting property is preserved under coproducts or quotients by null subspaces. We extend some results of A.G. Robertson and R.R. Smith on k-lifting property. Applications concern Kirchberg's conjecture and the Smith-Ward problem, which are shown to be equivalent with certain nuclearity type properties of low dimensional operator systems. © THETA, 2014.