Mathematische Annalen

, Volume 333, Issue 3, pp 471–484

The weak metric approximation property

Article

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 c0, constructed by Johnson and Schechtman, does not have the weak metric approximation property.

Mathematics Subject Classifications (2001)

46B04 46B20 46B28 46M05 47L05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsAgder University CollegeKristiansandNorway
  2. 2.Faculty of Mathematics and Computer ScienceTartu UniversityTartuEstonia

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