Local boundary representations for local operator systems

Abstract

In this paper, we show that the local boundary representations of a local operator system in a Fréchet locally C⁎-algebra on quantized Fréchet domains introduced by Arunkumar [6] are in fact local boundary representations on Hilbert spaces. Thus, the study of local boundary representations for local operator systems in Fréchet locally C⁎-algebras on quantized Fréchet domains is reduced to the study of boundary representations for operator systems.