Centre of a compact convex set
Functional Analysis
2022-03-07 v2
Abstract
We introduce the notion centre of a convex set and study the space of continuous affine functions on a compact convex set with a centre. We show that these spaces are precisely the dual of a base normed space in which the underlying base has a (unique) centre. We also characterize the corresponding base norm space. We obtain a condition on a compact, balanced, convex subset of a locally convex space so that the corresponding space of continuous affine functions on the convex set is an absolute order unit space. Similarly, we characterize a condition on the base with a centre of a base normed space so that the latter becomes an absolutely base normed space.
Cite
@article{arxiv.2201.07671,
title = {Centre of a compact convex set},
author = {Anil Kumar Karn},
journal= {arXiv preprint arXiv:2201.07671},
year = {2022}
}
Comments
16 pages