Factoring compact sets of operators

We describe a uniform factorization for the operators in a relatively compa ct set H subset of or equal to U(X, Y), where X,Y are Banach spaces and U i s a closed, injective, and surjective operator ideal. To be precise, we pro ve that there are a Banach space Z; operators u is an element of U(X, Z), v is an element of U(Z, Y); and a relatively compact set (H) over bar subset of U(Z, Z) such that every T is an element of H may be written in the form T = v (T) over baru, with (T) over bar is an element of (H) over bar. (C) 2001 Academic Press.