A Local Hahn-Banach Theorem and Its Applications
Functional Analysis
2018-09-07 v1
Abstract
An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space , there are sufficiently many continuous linear functionals to separate points of . In the paper, we establish a `local' version of this theorem. The result is applied to study the uo-dual of a Banach lattice that was recently introduced in [3]. We also provide a simplified approach to the measure-free characterization of uniform integrability established in [8].
Cite
@article{arxiv.1809.01795,
title = {A Local Hahn-Banach Theorem and Its Applications},
author = {Niushan Gao and Denny H. Leung and Foivos Xanthos},
journal= {arXiv preprint arXiv:1809.01795},
year = {2018}
}