Duality, reflexivity and atomic decompositions in Banach spaces
Volume 191 / 2009
Studia Mathematica 191 (2009), 67-80
MSC: Primary 41A65, 46B10; Secondary 42C15, 46B15.
DOI: 10.4064/sm191-1-5
Abstract
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.
