Quasi Hyperrigidity and Weak Peak Points for Non-Commutative Operator Systems

Abstract

In this article, we introduce the notions of weak boundary repre- sentation, quasi hyperrigidity and weak peak points in the non-commutative setting for operator systems in C* algebras. An analogue of Saskin theorem relating quasi hyperrigidity and weak Choquet boundary for particular classes of C* algebras is proved. We also show that, if an irreducible representation is a weak boundary representation and weak peak then it is a boundary repre- sentation. Several examples are provided to illustrate these notions. It is also observed that isometries on Hilbert spaces play an important role in the study of certain operator systems.