The strong approximation property and the weak bounded approximation property

摘要

We show that the strong approximation property (strong AP) (respectively, strong CAP) and the weak bounded approximation property (respectively, weak BCAP) are equivalent for every Banach space. This gives a negative answer to Oja's conjecture. As a consequence, we show that each of the spaces Co and ?_1 has a subspace which has the AP but fails to have the strong AP.