A Grothendieck compactness principle for the Mackey dual topology (original) (raw)

This work establishes a Grothendieck type compactness principle for the Mackey dual topology in Banach spaces. It extends the results of Grothendieck regarding norm compact subsets and their relationship to weak compactness to the context of weak* compact subsets in dual spaces. Additionally, it provides a characterization of Banach spaces that possess specific compactness properties related to null sequences and duals, drawing connections to known theorems such as the Schur property and the Banach-Dieudonné theorem.