Complemented copies of c0 in the vector-valued bounded function space

Assuming that Omega is a nonempty set and X is a Banach space, we study the presence of a copy of c(0) in X in relation to the existence of a complemented copy of c(0) in certain closed subspaces of the Banach space l(infinity)(Omega, X) of all bounded X-valued functions defined on Omega, equipped with the supremum norm. As an application we get a result of Diaz concerning complemented copies of c(0) in L-infinity(mu,X). A criterion for certain Banach spaces X to contain a complemented copy of c(0) whenever X contains a copy of c(0) is also included. (C) 1999 Academic Press.