Numerical range, dilation, and maximal operator systems

An operator system is a unital self-adjoint subspace of bounded linear operators. It is maximal if every positive linear map from it to another operator system is completely positive. In this paper, characterizations of maximal operator systems in terms of the joint numerical range are presented. New families of maximal operator systems are identified. These results admit formulations in terms of numerical range inclusion and dilation of operators that unify and extend earlier results on the topic.