On Mixed Transitivity of Arens Products

Abstract

Our matter is to investigate conditions of transitivity of Arens products in non regular Banach algebras. To this end we introduce the notion of links, i.e. some special elements of the second dual of a Banach algebra that allow a transitive passage between dierent Arens products. There will be two classes of links, both closed two sided ideals of the second dual space. We shall characterize these classes, determining some of their properties and giving a few examples.