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. 2009 Elsevier Inc. All rights reserved.
