Automatic continuity of *-morphisms between non-normed topological *- algebras (Q1174483)

This paper extends to locally convex algebras automatic continuity results known for Banach algebras. For instance it is shown that every \(*\)-morphism of a Fréchet locally convex \(*\)-algebra into a locally multiplicatively convex \(C^*\)-algebra is continuous. Thus every Fréchet lmc \(C^*\)-algebra has uniquely determined topology, and every lmc \(C^*\)-algebra has continuous involution. It is also shown that every \(*\)-representation of an involutive Fréchet \(Q\) lmc algebra is continuous, and if, additionally, the algebra has a bounded approximate identity then every positive linear form on it is continuous.