Positive operators and their applications on ordered vector spaces

Abstract

A vector space X is called an ordered vector space if for any elements x, y, z ∈ X and α ∈ R+, x ⪯ y implies x + z ≤ y + z and 0 ≤ x implies 0 ≤ αx. If in addition, X is a lattice, that is if for a pair {x, y} the inf{x, y} and sup{x, y} exists, then X is a Riesz space (or a vector lattice). In this study, we discuss Banach lattices, ordered Banach spaces, operators on these spaces and their applications in economics, fixed-point theory, differential and integral equations.