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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