Some dual Tauberian embeddings

Abstract

We show that if the famous construction of Davis, Figiel, Johnson and Pełczyński [1] is worked out on a weak-star compact set in a dual Banach space, then the resulting Banach space is a dual space. Next we apply this result to show that either a set is weak-star thick or it is contained in the operator range of a weak-star continuous Tauberian embedding. This result improves and, in some sense, completes the theory of thin sets and surjectivity described in [8].