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 Frechet locally C*-algebra on quantized Frechet domains introduced by Arunkumar [Local boundary representations of locally C*-algebras, J. Math. Anal. Appl. 515(2022),2,Paper No. 126416, 14pp.] are in fact local boundary representations on Hilbert spaces. Thus, the study of local boundary representations for local operator systems in Frechet locally C*-algebras on quantized Frechet domains is reduced to the study of boundary representations for operator systems.