In this paper we show how some known quasi *-algebras
can also be obtained through the construction of slight extensions of
nonclosable positive linear functionals defined on dense *-subalgebras
Ao of given topological *-algebras. Moreover, we consider also, for
each of the functionals we present, their absolutely convergent extensions
and the GNS *-representations of the quasi *-algebras arising in
the process of extension
