Positive bases in ordered subspaces with the Riesz decomposition property

Vasilios Katsikis, and Ioannis A. Polyrakis. "Positive bases in ordered subspaces with the Riesz decomposition property." Studia Mathematica 174.3 (2006): 233-253. <http://eudml.org/doc/286128>.

@article{VasiliosKatsikis2006,
abstract = {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.},
author = {Vasilios Katsikis, Ioannis A. Polyrakis},
journal = {Studia Mathematica},
keywords = {positive bases; unconditional bases; Riesz decomposition property; quasi-interior points},
language = {eng},
number = {3},
pages = {233-253},
title = {Positive bases in ordered subspaces with the Riesz decomposition property},
url = {http://eudml.org/doc/286128},
volume = {174},
year = {2006},
}

TY - JOUR
AU - Vasilios Katsikis
AU - Ioannis A. Polyrakis
TI - Positive bases in ordered subspaces with the Riesz decomposition property
JO - Studia Mathematica
PY - 2006
VL - 174
IS - 3
SP - 233
EP - 253
AB - 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.
LA - eng
KW - positive bases; unconditional bases; Riesz decomposition property; quasi-interior points
UR - http://eudml.org/doc/286128
ER -