Subspaces without the approximation property

It is proved that the Banach space l _p with 1≦p<2 contains a subspace without AP (the case 2<p≦∞ follows from the Enflo's construction and also from the present one). The result generalizes to the following one: if the supremum of types of X is strictly less than 2 or if the infimum of cotypes of X is strictly more than 2 then X contains a subspace without AP.