of and curves of
Author: Ioannis A. Polyrakis
Journal: Trans. Amer. Math. Soc. 348 (1996), 2793-2810
MSC (1991): Primary 46B42, 52A21, 15A48, 53A04
MathSciNet review: 1355300
Abstract: Let be linearly independent positive functions in , let be the vector subspace generated by the and let denote the curve of determined by the function , where . We establish that is a vector lattice under the induced ordering from if and only if there exists a convex polygon of with vertices containing the curve and having its vertices in the closure of the range of . We also present an algorithm which determines whether or not is a vector lattice and in case is a vector lattice it constructs a positive basis of . The results are also shown to be valid for general normed vector lattices.
Ioannis A. Polyrakis
Affiliation: Department of Mathematics, National Technical University, 157 80 Athens, Greece
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