Duality and o − O-structure in non reflexive Banach spaces

Luigi D'Onofrio, Carlo Sbordone, Roberta Schiattarella


Let E be a Banach space with a supremum type norm induced by a collection of functionals  ℒ ⊂ X* where X is a reflexive Banach space. Familiar spaces of this type are BMO, BV, C 0,α(0<α≤1), Lq,∾, for q>1. For most of these spaces E, the predual E* exists and can be defined by atomic decomposition of its elements. Another typical result, when it is possible to define a rich vanishing subspace E0E is the "two star theorem", namely (E0)*=E*. This fails for E=BV and E=C0,1=Lip.


Duality, Distance formula

Full Text:


DOI: https://doi.org/10.1478/AAPP.98S2A7

Copyright (c) 2020 Luigi D'Onofrio, Carlo Sbordone, Roberta Schiattarella

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.