Abstract. We investigate Arens regularity of semisimple Banach algebras $A$ which can be continuously embedded as dense subalgebras of Arens regular semisimple Banach algebras $B$. We assume that the algebras $A$ are right weakly completely continuous or weakly completely continuous.

AMS Subject Classification (1991): 46H20, 46H10, 46H35

Received September 23, 1994, and in revised form March 2, 1995. (Registered under 5695/2009.)