Embedding $\ell_2$ and $J$ into subspaces of $JT$ and $JT^*$

Spiros A. Argyros; Manuel Gonzalez; Pavlos Motakis

paper

Embedding $ℓ_{2}$ and $J$ into subspaces of $J T$ and $J T^{*}$

arXiv:2603.17886

Abstract

In the first part of the paper we show that every closed subspace of $J T$ or $J T^{*}$ contains $ℓ_{2}$ complemented in $J T$ or $J T^{*}$ respectively, and $J T$ contains uncomplemented copies of $ℓ_{2}$ . As a result, the predual $\B$ of $J T$ , as well as the spaces $J T$ and $J T^{*}$ , are subprojective and superprojective. In the second part, we prove that every weakly Cauchy sequence that is not weakly convergent in $J T$ has a subsequence equivalent to the basis of $J$ . Hence, every non-reflexive subspace of $J T$ contains an isomorphic copy of $J$ , and every Schauder basic sequence in $J T$ has a subsequence which is equivalent either to the basis of $ℓ_{2}$ or to the basis of $J$ . Moreover these subspaces may be selected to be complemented in $J T$ .

24 pages

Embedding ℓ2​ and J into subspaces of JT and JT∗

Abstract

Embedding $ℓ_{2}$ and $J$ into subspaces of $J T$ and $J T^{*}$