It is shown that there is a subspace of for which is isomorphic to such that does not have the approximation property. On the other hand, for there is a subspace of such that does not have the approximation property (AP) but the quotient space is isomorphic to . The result is obtained by defining random "Enflo-Davie spaces" which with full probability fail AP for all and have AP for all . For 2, are isomorphic to .
Cite this article
A. Szankowski, Three-space problems for the approximation property. J. Eur. Math. Soc. 11 (2009), no. 2, pp. 273–282DOI 10.4171/JEMS/150