Resumen de Uniform Boundedness and Twisted Sums of Banach Spaces

Félix Cabello Sánchez , Jesús María Fernández Castillo

• We construct a Banach space X admitting an uncomplemented copy of l1 so that X/l1 = c0. To do that we study the uniform boundedness principles that arise when one considers exact sequences of Banach spaces; as well as several elements of homological algebra applied to the construction of nontrivial twisted sum of Banach spaces. The combination of both elements allows one to determine the existence of nontrivial twisted sums for almost all combinations of classical Banach spaces.