[Banach] Abstract of a paper by Fabio Jose Bertoloto

This is an announcement for the paper "Duality of certain Banach spaces of vector-valued holomorphic functions" by Fabio Jose Bertoloto.

Abstract: In this work we study the vector-valued Hardy spaces H p (D; F ) (1 ≤ p ≤ ∞) 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 ∈ (1, ∞) conjugate indices) if and only if F has the UMDP.

Archive classification: math.FA

Mathematics Subject Classification: 46G20, 46G10, 30H10

Submitted from: bertoloto@famat.ufu.br

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1203.5322

or

http://arXiv.org/abs/1203.5322