Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Finite-dimensional lattice-subspaces
of $C(\Omega )$ and curves of $\mathbb R^n$

Author: Ioannis A. Polyrakis
Journal: Trans. Amer. Math. Soc. 348 (1996), 2793-2810
MSC (1991): Primary 46B42, 52A21, 15A48, 53A04
MathSciNet review: 1355300
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $x_1,\dotsc ,x_n$ 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 $\mathbb R^n$ determined by the function $\beta (t)=\frac {1}{z(t)} (x_1(t),x_2(t),\dotsc ,x_n(t))$, where $z(t)=x_1(t)+x_2(t)+\dotsb +x_n(t)$. 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 $\mathbb R^n$ 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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 46B42, 52A21, 15A48, 53A04

Retrieve articles in all journals with MSC (1991): 46B42, 52A21, 15A48, 53A04

Additional Information

Ioannis A. Polyrakis
Affiliation: Department of Mathematics, National Technical University, 157 80 Athens, Greece

PII: S 0002-9947(96)01639-X
Received by editor(s): April 24, 1995
Additional Notes: This research was supported in part by the NATO Collaborative Research Grant #941059.
Article copyright: © Copyright 1996 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia