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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....
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