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Three-space problems for the approximation property

A. Szankowski — 2009

Journal of the European Mathematical Society

It is shown that there is a subspace Z q of q for 1 < q < 2 which is isomorphic to q such that q / Z q does not have the approximation property. On the other hand, for 2 < p < there is a subspace Y p of p such that Y p does not have the approximation property (AP) but the quotient space p / Y p is isomorphic to p . The result is obtained by defining random “Enflo-Davie spaces” Y p which with full probability fail AP for all 2 < p and have AP for all 1 p 2 . For 1 < p 2 , Y p are isomorphic to p .

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