Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4624024 | Journal of Mathematical Analysis and Applications | 2006 | 14 Pages |
Abstract
Based on a new reformulation of the bounded approximation property, we develop a unified approach to the lifting of bounded approximation properties from a Banach space X to its dual X*. This encompasses cases when X has the unique extension property or X is extendably locally reflexive. In particular, it is shown that the unique extension property of X permits to lift the metric A-approximation property from X to X*, for any operator ideal A, and that there exists a Banach space X such that X,X**,… are extendably locally reflexive, but X*,X***,… are not.
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