Atomic decomposition for preduals of some Banach spaces
Luigi D'Onofrio, Carlo Sbordone, Roberta Schiattarella

Abstract. Given a Banach space E with a supremum type norm induced by a sequence L=(L_j) of linear forms L_j: X→ R on the Banach space X, we prove that if the unit ball B_X 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.

Rend. Mat. Appl. (7) 41 (2020) 265-274; pdf