Strongly normal cones and the midpoint locally uniform rotundity

TL;DR

This paper introduces a method to construct positive cones in Banach spaces that are normal but not strongly normal, highlighting nuanced geometric properties of these cones.

Contribution

It provides a novel construction method for positive cones that are normal but lack strong normality in Banach spaces.

Findings

Constructed examples of normal but not strongly normal cones

Highlighted differences between normality and strong normality in cones

Enhanced understanding of cone geometry in Banach spaces

Abstract

We give the method of construction of normal but not strongly normal positive cones in Banach space.