Order extreme points and solid convex hulls

2019/07/01 by Timur Oikhberg, Oikhberg, Timur, Mary Angelica Tursi +1
Computer Science · Mathematics · #46B22 #46B42 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1907.00660

openalex publication_date 2019/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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