By a well-known result of Grothendieck, a Banach space X has the approximation property if and only if, for every Banach space Y , every weak\*-weak continuous compact operator T : X \* → Y can be uniformly approximated by finite rank operators from X ⊗ Y . We prove the following "metric" version of
✦ LIBER ✦
The weak metric approximation property
✍ Scribed by Åsvald Lima; Eve Oja
- Publisher
- Springer
- Year
- 2005
- Tongue
- English
- Weight
- 192 KB
- Volume
- 333
- Category
- Article
- ISSN
- 0025-5831
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## Abstract We establish necessary and sufficient conditions involving trace mappings and Hahn–Banach extension operators for a Banach space to have metric or metric compact approximation properties. We also study metric approximation properties for dual spaces. As an application, alternative (hope
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