Tensor products of hyperrigid operator systems

Abstract

In this article, we prove that the tensor product of two hyperrigid operator systems is hyperrigid in the spatial tensor product of $C^{\ast }$-algebras. We deduce this by establishing that the unique extension property for unital completely positive maps on operator systems carry over to tensor products such maps defined on the tensor product operator systems. Hopenwasser’s result about the tensor product of boundary representations follows as a special case. We also provide examples to illustrate the hyperrigidity property of tensor products of operator systems.