Positive bases in ordered subspaces with the Riesz decomposition property

• Autorzy: Vasilios Katsikis , Ioannis A. Polyrakis
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 46B15: Summability and bases
• 46B42: Banach lattices
• 46B40: Ordered normed spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 174
• Numer: 3
• Strony: 233-253

Daty

wydano

2006

Twórcy

autor

Vasilios Katsikis

• Department of Mathematics, National Technical University of Athens, Zografou Campus 157 80, Athens, Greece

autor

Ioannis A. Polyrakis

• Department of Mathematics, National Technical University of Athens, Zografou Campus 157 80, Athens, Greece

Identyfikatory

DOI

10.4064/sm174-3-2