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## Studia Mathematica

2006 | 174 | 3 | 233-253
Tytuł artykułu

### Positive bases in ordered subspaces with the Riesz decomposition property

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EN
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EN
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.
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Tom
Numer
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233-253
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wydano
2006
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autor
• Department of Mathematics, National Technical University of Athens, Zografou Campus 157 80, Athens, Greece
autor
• Department of Mathematics, National Technical University of Athens, Zografou Campus 157 80, Athens, Greece
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