JournalsjemsVol. 11 , No. 2DOI 10.4171/jems/150

Three-space problems for the approximation property

  • A. Szankowski

    The Hebrew University of Jerusalem, Israel
Three-space problems for the approximation property cover

Abstract

It is shown that there is a subspace ZqZ_q of q\ell_q for 1<q<21<q<2 which is isomorphic to q\ell_q such that q/Zq\ell_q/Z_q does not have the approximation property. On the other hand, for 2<p<2<p<\infty there is a subspace YpY_p of p\ell_p such that YpY_p does not have the approximation property (AP) but the quotient space p/Yp\ell_p/Y_p is isomorphic to p\ell_p . The result is obtained by defining random "Enflo-Davie spaces" YpY_p which with full probability fail AP for all 2<p2 < p\leq\infty and have AP for all 1p21 \leq p \leq 2. For 1<p1 < p \leq 2, YpY_p are isomorphic to p\ell_p.