Positive bases in ordered subspaces with the Riesz decomposition property
In this article we suppose that E is an ordered Banach space whose positive cone is defined by a countable family of positive continuous linear functionals on E, i.e. E₊ = x ∈ E | for each i, and we study the existence of positive (Schauder) bases in ordered subspaces X of E with the Riesz decomposition property. We consider the elements x of E as sequences and we develop a process of successive decompositions of a quasi-interior point of X₊ which at each step gives elements with smaller support....