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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 , are isomorphic to .
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