Quasi hyperrigidity and weak peak points for non-commutative operator systems

In this article, we introduce the notions of weak boundary representation, quasi hyperrigidity and weak peak points in the non-commutative setting for operator systems in $$C^*$$C∗-algebras. An analogue of Saskin’s theorem relating quasi hyperrigidity and weak Choquet boundary for particular classes of $$C^*$$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 representation. Several examples are provided to illustrate these notions.