Factoring Compact Sets of Operators

We describe a uniform factorization for the operators in a relatively compact set H UŽX, Y., where X, Y are Banach spaces and U is a closed, injective, and surjective operator ideal. To be precise, we prove that there are a Banach space Z; operators u UŽX, Z., UŽZ, Y.; and a relatively compact set H UŽZ, Z. such that every T H may be written in the form T Tu, with T H.