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Positive bases in ordered subspaces with the Riesz decomposition property

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Katsikis V., Polyrakis I.

Studia Mathematica

2006

tom 174

nr 3

233-253

In this article we suppose that E is an ordered Banach space whose positive cone is defined by a countable family $ℱ = {f_{i} | i ∈ ℕ}$ of positive continuous linear functionals on E, i.e. E₊ = {x ∈ E | $f_{i}(x) ≥ 0$ 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. As a result we obtain elements of X₊ with minimal support and we prove that they define a positive basis of X which is also unconditional. In the first section we study ordered normed spaces with the Riesz decomposition property.

Ograniczanie wyników

1 Studia Mathematica

1 Katsikis V.

1 Polyrakis I.

1 2006

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Positive bases in ordered subspaces with the Riesz decomposition property