Resumen de Sobczyk's Theorems from A to B

David Yost, Félix Cabello Sánchez , Jesús María Fernández Castillo

• Sobczyk's theorem is usually stated as: every copy of c0 inside a separable Banach space is complemented by a projection with norm at most 2. Nevertheless, our understanding is not complete until we also recall: and c0 is not complemented in l8. Now the limits of the phenomenon are set: although c0 is complemented in separable superspaces, it is not necessarily complemented in a non-separable superspace, such as l8.