Jordan Decomposition for WBV-functions in Ordered Normed Spaces

Abstract

In this paper, we define two relations one by orthogonality in vector lattices named as strong relation and the other by bounded linear functionals in normed spaces named as weak relation. It turns out that strong relation is an equivalence relation. We study some of the characterizations of these relations. Given a non-zero element in a normed space, we construct an extensible cone which makes that normed space, an ordered normed space. This extensible cone induces the weak relation in the normed space. Later, we prove a Jordan Decomposition Theorem in a normed space by the weak relation induced by the extensible cone.