Well-behaved unbounded operator representations and unbounded C*-seminorms

Abstract

The first purpose is to characterize the existence of well-behaved $*$ -representations of locally convex $*$ -algebras by unbounded $C^*$ -seminorms. The second is to define the notion of spectral $*$ -representations and to characterize the existence of spectral well-behaved $*$ -representations by unbounded $C^*$ -seminorms.