Lifting bounded approximation properties from Banach spaces to their dual spaces |
| |
Authors: | Eve Oja |
| |
Affiliation: | Faculty of Mathematics and Computer Science, Tartu University, J. Liivi 2, EE-50409 Tartu, Estonia |
| |
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. |
| |
Keywords: | Bounded approximation properties Operator ideals Unique extension property Extendable local reflexivity |
本文献已被 ScienceDirect 等数据库收录! |
|