The weak metric approximation property and ideals of operators

We study the weak metric approximation property introduced by Lima and Oja. We show that a Banach space X has the weak metric approximation property if and only if F(Y,X), the space of finite rank operators, is an ideal inW(Y,X∗∗), the space of weakly compact operators for all Banach spaces Y . © 2007 Elsevier Inc. All rights reserved