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.