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

摘要

In this paper, we address the problem of automatic continuity of homomorphismsin some topological non associative * -algebras. To do this, we introduce andstudy 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.