Positive bases in ordered subspaces with the Riesz decomposition property

Katsikis, V; Polyrakis, IA

dc.contributor.author	Katsikis, V	en
dc.contributor.author	Polyrakis, IA	en
dc.date.accessioned	2014-03-01T01:24:52Z
dc.date.available	2014-03-01T01:24:52Z
dc.date.issued	2006	en
dc.identifier.issn	0039-3223	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17476
dc.subject	Positive bases	en
dc.subject	Quasi-interior points	en
dc.subject	Riesz decomposition property	en
dc.subject	Unconditional bases	en
dc.subject.classification	Mathematics	en
dc.subject.other	BANACH-SPACES	en
dc.title	Positive bases in ordered subspaces with the Riesz decomposition property	en
heal.type	journalArticle	en
heal.identifier.primary	10.4064/sm174-3-2	en
heal.identifier.secondary	http://dx.doi.org/10.4064/sm174-3-2	en
heal.language	English	en
heal.publicationDate	2006	en
heal.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) vertical bar i is an element of N} of positive continuous linear functionals on E, i.e. E+ = {x is an element of E vertical bar 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.	en
heal.publisher	POLISH ACAD SCIENCES INST MATHEMATICS	en
heal.journalName	Studia Mathematica	en
dc.identifier.doi	10.4064/sm174-3-2	en
dc.identifier.isi	ISI:000240691200002	en
dc.identifier.volume	174	en
dc.identifier.issue	3	en
dc.identifier.spage	233	en
dc.identifier.epage	253	en