Duality of certain Banach spaces of vector-valued holomorphic functions
Functional Analysis
2012-03-26 v1
Abstract
In this work we study the vector-valued Hardy spaces H p (D; F) (1 \leq p \leq \infty) and their relationship with RNP, ARNP and the UMDP properties. By following the approach of Taylor in the scalar-valued case, we prove that, when F and F have the ARNP property, then H p (D; F) and H q (D; F) are canonically topologically isomorphic (for p, q \in (1, \infty) conjugate indices) if and only if F has the UMDP.
Keywords
Cite
@article{arxiv.1203.5322,
title = {Duality of certain Banach spaces of vector-valued holomorphic functions},
author = {Fábio José Bertoloto},
journal= {arXiv preprint arXiv:1203.5322},
year = {2012}
}