Abstract:Conditions are given for Banach algebras A and Banach algebras B which insure that every homomorphism T from A into B is automatic continuous. Similar results are obtained for derivations which either map the algebra A into itself.
Nous étudions les problèmes de continuité automatique dans des algèbres de Banach avec involutions. Nous obtenons aussi des nouveoux résultats concernant☆-idéals des☆-algèbres.We study the automatic continuity problems for Banach algebras with involutions. We also obtain some new results concerning☆-ideals of☆-algebras.
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.
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