Structure of sets of strong subdifferentiability in dual $L^1$-spaces
Functional Analysis
2020-10-27 v1
Abstract
In this article, we analyse the structure of finite dimensional subspaces of the set of points of strong subdifferentiability in a dual space. In a dual space, such a subspace is in the discrete part of the Yoshida-Hewitt type decomposition. In this set up, any Banach space consisting of points of strong subdifferentiability is necessarily finite dimensional. Our results also lead to streamlined and new proofs of results from the study of strong proximinality for subspaces of finite co-dimension in a Banach space.
Keywords
Cite
@article{arxiv.2010.13595,
title = {Structure of sets of strong subdifferentiability in dual $L^1$-spaces},
author = {C. R. Jayanarayanan and T. S. S. R. K. Rao},
journal= {arXiv preprint arXiv:2010.13595},
year = {2020}
}
Comments
To appear in Journal of Convex Analysis