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

Abstract Quasi *-algebras possessing a sufficient family $$\mathcal {M}$$ M of invariant positive sesquilinear forms carry several topologies related to $$\mathcal {M}$$ 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 $$\mathcal {M}$$ M , is a dense C*-algebra.