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

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.