Resumen de Uniform-to-proper duality of geometric properties of Banach spaces and their ultrapowers
In this note various geometric properties of a Banach space X are characterized by means of weaker corresponding geometric properties involving an ultrapower XU. The characterizations do not depend on the particular choice of the free ultrafilter U on N. For example, a point x∈SX is an MLUR point if and only if ȷ(x) (given by the canonical inclusion ȷ:X→XU) in BXU is an extreme point; a point x∈SX is LUR if and only if ȷ(x) is not contained in any non-degenerate line segment of SXU; a Banach space X is URED if and only if there are no x,y∈SXU, x≠y, with x−y∈ȷ(X).
