Topological aspects of quasi *-algebras with sufficiently many *-representations

Abstract

Quasi *-algebras possessing a sufficient family $\mathcal{M}$ of invariant positive sesquilinear forms carry several topologies related to $\mathcal{M}$ which make every *-representation continuous. This leads to define the class of locally convex quasi GA*-algebras whose main feature consists in the fact that the family of their bounded elements, with respect to the family $\mathcal{M}$, is a dense C*-algebra.