Lifting some approximation properties from a dual space X0 to the Banach space X

Abstract

For a fixed Banach operator ideal A, we characterize A-compact sets (in the sense of Carl and Stephani) that are determined by c0 via the Banach composition ideal A ◦K∞, with K∞ the Banach ideal of Fourie and Swart. This characterization allows us to relate KA-approximation properties on a Banach space and KB-approximation properties on its dual space, where A and B are ideals linked by some classical procedures. These approximation properties have been widely studied in several papers in the last years