On automatic continuity of linear operators in certain classes of non-associative topological algebras

Abstract

In this paper, we address the problem of automatic continuity of homomorphisms in some topological non associative * -algebras. To do this, we introduce and study on a non-associative algebra equipped with an involution * a notion we call * -semi-simplicity. It is based on the study of certain sided ideals called * -ideals.