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. 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-3-2,
author = {Vasilios Katsikis and Ioannis A. Polyrakis},
title = {Positive bases in ordered subspaces with the Riesz decomposition property},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {233-253},
zbl = {1103.46013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-3-2}
}
Vasilios Katsikis; Ioannis A. Polyrakis. Positive bases in ordered subspaces with the Riesz decomposition property. Studia Mathematica, Tome 173 (2006) pp. 233-253. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-3-2/