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Positive bases in ordered subspaces with the Riesz decomposition property

Vasilios Katsikis; Ioannis A. Polyrakis — 2006

Studia Mathematica

In this article we suppose that E is an ordered Banach space whose positive cone is defined by a countable family $ℱ = f_{i} | i \in ℕ$ of positive continuous linear functionals on E, i.e. E₊ = x ∈ E | $f_{i} (x) \geq 0$ 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 $x = (f_{i} (x))$ 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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