On the Local Boundary Representations of Locally \(C^*\)-Algebras

In this paper, we study the non-commutative Choquet boundary for systems of unbounded operators on a Hilbert space. To do this, we introduce the notion of local boundary representations for local operator systems in locally \(C^*\) $C^{\ast }$ -algebras and provide some characterizations on Fréchet quantized domains.