  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.
