Atomic decomposition for preduals of some Banach spaces

Abstract

Given a Banach space E with a supremum type norm induced by a sequence L=(Lj) of linear forms Lj: X→ R on the Banach space X, we prove that if the unit ball BX is σ(X, L)- compact then E has a predual E* with an atomic decomposition. We extend results from [7] where X is assumed a reflexive Banach space.

Keywords

• dual and predual
• atomic decomposition.