Order extreme points and solid convex hulls
Functional Analysis
2020-02-11 v2
Abstract
We consider the "order" analogues of some classical notions of Banach space geometry: extreme points and convex hulls. A Hahn-Banach type separation result is obtained, which allows us to establish an "order" Krein-Milman Theorem. We show that the unit ball of any infinite dimensional reflexive space contains uncountably many order extreme points, and investigate the set of positive norm-attaining functionals. Finally,we introduce the "solid" version of the Krein-Milman Property, and show it is equivalent to the Radon-Nikodym Property.
Cite
@article{arxiv.1907.00660,
title = {Order extreme points and solid convex hulls},
author = {Timur Oikhberg and Mary Angelica Tursi},
journal= {arXiv preprint arXiv:1907.00660},
year = {2020}
}
Comments
19 pages