Asplund spaces characterized by rich families and separable reduction of Frechet subdifferentiability

Abstract

Asplund property of a Banach space X is characterized by the existence of a rich family, in the product XxX*, consisting of some carefully chosen separable subspaces. This structural result is then used to add a lot of precision and simplicity to the known separable reductions of Fréchet subdifferentials.

Keywords

• Asplund space
• Rich family
• Separable reduction
• Fréchet subdifferential