On the subspaces of JF and JT with non-separable dual ✩

It is proved that every subspace of James Tree space (JT) with non-separable dual contains an isomorph of James Tree complemented in JT. This yields that every complemented subspace of JT with non-separable dual is isomorphic to JT. A new JT like space denoted as TF is defined. It is shown that every subspace of James Function space (JF) with non-separable dual contains an isomorph of TF. The later yields that every subspace of JF with non-separable dual contains isomorphs of c0 and p for 2 p <∞. The analogues of the above results for bounded linear operators are also proved. © 2007 Elsevier Inc. All rights reserved