We show that the set of all separable Banach spaces that have the bounded approximation property (BAP) is a Borel subset of the set of all closed subspaces of $C(\Delta)$, where $\Delta$ is the Cantor set, equipped with the standard Effros-Borel structure. Also, we prove that if $X$ is a separable Banach space with a norming M-basis $\{e_{i} , e_{i}^{*} \}_{i=1}^{\infty}$ and $E_{u}=\overline{span} \{e_{i};\,\,i \in u\}$ for $u \in \Delta,$ then the set $\{u \in \Delta;\,\,E_{u}\,\,has\,\,a\,\,FDD\}$ is comeager in $\Delta$.

Title

HOUSTON JOURNAL OF MATHEMATICS

Publisher

University of Houston, Houston, Texas ISSN 0362-1588

Publisher Country

United States of America

Indexing

Thomson Reuters

Impact Factor

0.273

Publication Type

Both (Printed and Online)

Volume

43

Year

2017

Pages

395-401