Z-Hyperrigidity and Z-boundary representations

In this article, we introduce the notions of Z-finite representations and Z-separation property of representations for operator Z-systems generating C∗-algebras. We use these notions to characterize the Z-boundary representations for operator Z-systems. We introduce Z-hyperrigidity of operator Z-systems. We investigate an analogue version of Saskin’s theorem in the setting of operator Z-systems generating C∗-algebras.