On the three-space problem for the Dunford-Pettis property

Abstract

A Banach space X is called a twisted sum of the Banach spaces Y and Z if it has a subspace isomorphic to Y in such a way that the corresponding quotient is isomorphic to Z. In this paper we study twisted sums of Banach spaces with either have the Dunford-Pettis property, are co-saturated or /i-saturated. Amongst other things, we show that every Banach space is a complemented subspace of a twisted sum of two Banach spaces with the Dunford-Pettis property.

Three-Space Problems for Polynomial Properties in Banach Spaces

“…The proof is based on a version of a result in [11]. We include a proof for the sake of completeness.…”