Almost all positive continuous linear functionals can be extended

Journal article (2022)

Authors

J. van Dobben de Bruyn Discrete Mathematics and Optimization - EEMCS
Research Group
Discrete Mathematics and Optimization (EEMCS) (TU Delft)
Copyright: © 2022 J. van Dobben de Bruyn
DOI: https://doi.org/10.1007/s11117-022-00881-6
More Info
expand_more

Published Date

2022

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Discrete Mathematics and Optimization

Abstract

Let F be an ordered topological vector space (over R) whose positive cone F+ is weakly closed, and let E⊆ F be a subspace. We prove that the set of positive continuous linear functionals on E that can be extended (positively and continuously) to F is weak-∗ dense in the topological dual wedge E+′. Furthermore, we show that this result cannot be generalized to arbitrary positive operators, even in finite-dimensional spaces.