“…In fact, if the closed subspace X ⊂ c 0 fails to have the A.P., then by [36,Theorem 1.e.4] there is a Banach space Y and an operator T ∈ K(Y, X) \ A(Y, X). By a compact factorisation theorem of Terzioğlu [52] (see also Randtke [45]) we may factor T compactly through a closed subspace of c 0 , that is, there is a closed subspace Z 0 ⊂ c 0 and A ∈ K(Y, Z 0 ), B ∈ K(Z 0 , X) such that T = BA. Consider Z = Z 0 ⊕ X ⊂ c 0 and define U ∈ L(Z) by U (x, y) = (0, Bx), (x, y) ∈ Z.…”