De la recherche pétrolière à la géométrie des espaces de Banach en passant par les paraproduits
Dentability and finite-dimensional decompositions
Deux espaces de Banach et leurs modèles étalés
Differentiability of Lipschitzian mappings between Banach spaces
Domination and equivalence of sequences of subspaces in dual spaces
Duality, reflexivity and atomic decompositions in Banach spaces
We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of "shrinking" and "boundedly complete" Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. We also characterize the reflexivity of a Banach space in terms of properties of its atomic decompositions....