Finite-dimensional lattice-subspaces of C(Ω) and curves of ℝn

Polyrakis, IA

dc.contributor.author	Polyrakis, IA	en
dc.date.accessioned	2014-03-01T01:44:44Z
dc.date.available	2014-03-01T01:44:44Z
dc.date.issued	1996	en
dc.identifier.issn	00029947	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/24463
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-21344455048&partnerID=40&md5=43a65d842abf39e9aa380493fe2b1d0d	en
dc.title	Finite-dimensional lattice-subspaces of C(Ω) and curves of ℝn	en
heal.type	journalArticle	en
heal.publicationDate	1996	en
heal.abstract	Let x1, . . . , xn be linearly independent positive functions in C(Ω), let X be the vector subspace generated by the xi and let β denote the curve of ℝn determined by the function β(t) = 1/z(t)(x1(t),x2(t), . . . , xn(t)), where z(t) = x1(t) +x2(t) + ⋯ + xn(t). We establish that X is a vector lattice under the induced ordering from C(Ω) if and only if there exists a convex polygon of ℝn with n vertices containing the curve β and having its vertices in the closure of the range of β. We also present an algorithm which determines whether or not X is a vector lattice and in case X is a vector lattice it constructs a positive basis of X. The results are also shown to be valid for general normed vector lattices. © 1996 American Mathematical Society.	en
heal.journalName	Transactions of the American Mathematical Society	en
dc.identifier.volume	348	en
dc.identifier.issue	7	en
dc.identifier.spage	2793	en
dc.identifier.epage	2810	en