Complemented Copies of c in the Vector-Valued 0 Bounded Function SpaceU

Assuming that V is a nonempty set and X is a Banach space, we study the presence of a copy of c0 in X in relation to the existence of a complemented copy of c0 in certain closed subspaces of the Banach space l` V, X.of all bounded X-valued functions defined on V, equipped with the supremum norm. As an application we get a result of D´ıaz concerning complemented copies of c0 in L m,X.. A criterion for certain Banach spaces X to contain a complemented ` copy of c0whenever X contains a copy of c0is also included.