THE WEAK METRIC APPROXIMATION PROPERTY

Abstract. We introduce and investigate the weak metric approxima-tion property of Banach spaces which is strictly stronger than the ap-proximation property and at least formally weaker than the metric ap-proximation property. Among others, we show that if a Banach space has the approximation property and is 1-complemented in its bidual, then it has the weak metric approximation property. We also study the lifting of the weak metric approximation property from Banach spaces to their dual spaces. This enables us, in particular, to show that the subspace of c0, constructed by Johnson and Schechtman, does not have the weak metric approximation property. 1