Complementably universal Banach spaces, II

The two main results are:A.If a Banach space X is complementably universal for all subspaces of c0 which have the bounded approximation property, then X∗ is non-separable (and hence X does not embed into c0).B.There is no separable Banach space X such that every compact operator (between Banach spaces) factors through X. Theorem B solves a problem that dates from the 1970s.