On Twisted Sums of Sequence Spaces

Abstract

 We prove the existence of non trivial twisted sums involving the p^th James space J_p(1 < p < 1), the Johnson-Lindenstrauss space JL; the James tree space JT , the Tsirelson’s space T and the Argyros and Deliyanni space AD . We also present non trivial twisted sums involving their duals and biduals. We show that there are strictly singular quasi-linear maps from the spaces T ;T^* ; AD and JT into C[0; 1]. We discuss the Pelczynski’s property(u) for the twisted sums involving these spaces which extends a pthJames-Schreier spaces V_p(1 < p <1) or J_2.