, Volume 333, Issue 3, pp 471-484
Date: 23 Aug 2005

The weak metric approximation property

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Abstract

We introduce and investigate the weak metric approximation property of Banach spaces which is strictly stronger than the approximation property and at least formally weaker than the metric approximation 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 c 0, constructed by Johnson and Schechtman, does not have the weak metric approximation property.

The research of the second-named author was partially supported by Estonian Science Foundation Grant 5704 and the Norwegian Academy of Science and Letters.