The Jordan decomposition of bounded variation functions valued in vector spaces

Abstract

In this paper we show the Jordan decomposition for bounded variation functions withvalues in Riesz spaces. Through an equivalence relation, we prove that this decomposition is satisfiedfor functions valued in Hilbert spaces. This result is a generalization of the real case. Moreover, weprove that, in general, the Jordan decomposition is not satisfied for vector-valued functions.

Keywords

• Jordan decomposition| bounded variation function| Hilbert spaces| Riesz spaces| normed spaces