Banach spaces

In the recent paper by <.zeta.>. Lima, O. Nygaard and E. Oja it was proved that if X has the CAP then for all Banach spaces Y, K(Y, X) is an ideal in W(Y, X). But this last property does not characte rize Banach spaces with the CAP. The plan is that Vegard Lima will continue to investigate the connection between diffferent approximation properties and subspaces of operators which are ideals. Special emphasize will be put on results that can give a better understanding of the difference between the AP and the CAP. He will look at the example by Willis of the reflexive Banach Z# which has the MCAP but not the AP. Is it possible to simplify the proof or give more examples usi ng our methods? Vegard Lima will try to findbetter results for the CAP.