2018/09/06 by Niushan Gao, Denny H. Leung, Gao, Niushan +3
Mathematics · #46A20 #46A22 #60A10 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46A20 #msc:46A22 #msc:60A10
paper · pdf · doi:10.48550/arxiv.1809.01795
arxiv created 2018/09/06 · arxiv updated 2018/09/07
An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space X, there are sufficiently many continuous linear functionals to separate points of X. 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].