Finite-dimensional lattice-subspaces of C(Omega) and curves of R(n)

Polyrakis, IA

dc.contributor.author	Polyrakis, IA	en
dc.date.accessioned	2014-03-01T01:45:07Z
dc.date.available	2014-03-01T01:45:07Z
dc.date.issued	1996	en
dc.identifier.issn	0002-9947	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/24549
dc.subject.classification	Mathematics	en
dc.title	Finite-dimensional lattice-subspaces of C(Omega) and curves of R(n)	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1996	en
heal.abstract	Let x(1),...,x(n) be linearly independent positive functions in C(Omega), let X be the vector subspace generated by the x(i) and let beta denote the curve of R(n) determined by the function beta(t) = 1/z(t)(x(1)(t),x(2)(t),...,x(n)(t)), where z(t) = x(1)(t) + x(2)(t) +...+ x(n)(t). We establish that X is a vector lattice under the induced ordering from C(Omega) if and only if there exists a convex polygon of R(n) with n vertices containing the curve beta and having its vertices in the closure of the range of beta. 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.	en
heal.publisher	AMER MATHEMATICAL SOC	en
heal.journalName	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY	en
dc.identifier.isi	ISI:A1996UX91000014	en
dc.identifier.volume	348	en
dc.identifier.issue	7	en
dc.identifier.spage	2793	en
dc.identifier.epage	2810	en