Uniformly summing sets of operators on spaces of vector-valued continuous functions

Let X, Y be Banach spaces. We say that a set M subset of Pi(p)(X,Y) is uniformly p-summing if the series (n)Sigma parallel to Tx(n)parallel to(p) is uniformly convergent for T is an element of M whenever (x(n)) belongs to l(w)(p)(X). We consider uniformly summing sets of operators defined as C(Omega, X)-space and prove, in case X does not contain a copy of c(0), that M is uniformly summing iff M-# = {T# : C(Omega) ->Pi(1)(X,Y) : T is an element of M} is, where T(phi x) = T-#phi)x for all phi is an element of C(Omega) and x is an element of X. We also characterize the sets M with the property that M-# is uniformly summing viewed in Pi(1)(C(Omega), L(X,Y)).