2026/03/18 by Spiros A. Argyros, Manuel Gonzalez, Pavlos Motakis
Mathematics · #math.FA
In the first part of the paper we show that every closed subspace of JT or JT^* contains ℓ2 complemented in JT or JT^* respectively, and JT contains uncomplemented copies of ℓ2. As a result, the predual \B of JT, as well as the spaces JT and JT^*, are subprojective and superprojective. In the second part, we prove that every weakly Cauchy sequence that is not weakly convergent in JT has a subsequence equivalent to the basis of J. Hence, every non-reflexive subspace of JT contains an isomorphic copy of J, and every Schauder basic sequence in JT has a subsequence which is equivalent either to the basis of ℓ2 or to the basis of J. Moreover these subspaces may be selected to be complemented in JT.