It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property. 1991 Mathematics Subject Classification: primary 46B28; secondary 46B10

In this paper, the notion of the bounded compact approximation property (BCAP) of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of L∞ with the bounded compact approximation property, then L∞/X has the bounded compact approximation property. We also show that X∗ has the λ-BCAP with conjugate operators if and only if the pair (X,Y ) has the λ-BCAP for each...