Resumen de Linear extensions, almost isometries, and diameter two

Trond A. Abrahamsen

• Heinrich, Mankiewicz, Sims, and Yost proved that every separable subspace of a Banach space Y is contained in a separable ideal in Y . We improve this result by replacing the term \ideal" with the term \almost isometric ideal". As a consequence of this we obtain, in terms of subspaces, characterizations of diameter 2 properties, the Daugavet property along with the properties of being an almost square space and an octahedral space.