Arens regularity of certain Banach algebras which are ideals of a Banach algebra

Abstract

The question of Arens regularity for a dual A* -algebra which is a dense two-sided ideal of a B* -algebra has been discussed by Wong and by Alexander. We consider the Arens regularity of some Banach algebras which are denseideals of Arens regular Banach algebras to prove, among other results, that any commutative A* -algebra which is an ideal of its completion in the auxiliary norm is Arens regular.