Narrow Results

Motivated by an observation of Namioka and Phelps on an approximation property of order unit spaces, we introduce the $p$-tensor product and the $m$-tensor product of two compact matrix convex sets. We define a new approximation property for operator systems, and give a characterization using the $p$- and $m$-tensor products in the spirit of Grothendieck. Thus, an operator system has the operator system approximation property if and only if it is $(p,m)$-nuclear in a natural sense.