Uniformly factoring weakly compact operators

Let X and Y be separable Banach spaces. Suppose Y either has a shrinking basis or Y   is isomorphic to C(2N)C(2N) and AA is a subset of weakly compact operators from X to Y which is analytic in the strong operator topology. We prove that there is a reflexive space with a basis Z   such that every T∈AT∈A factors through Z  . Likewise, we prove that if A⊂L(X,C(2N))A⊂L(X,C(2N)) is a set of operators whose adjoints have separable range and is analytic in the strong operator topology then there is a Banach space Z   with separable dual such that every T∈AT∈A factors through Z. Finally we prove a uniform version of this result in which we allow the domain and range spaces to vary.