# Ordered vector spaces and linear operators

@inproceedings{Cristescu1976OrderedVS, title={Ordered vector spaces and linear operators}, author={Romulus Cristescu and Silviu Teleman and John C. Hammel}, year={1976} }

An ordered vector space is just that-a set with both a (real) vector space structure and an order relation which satisfy desirable compatibility conditions. Specialization by requiring that the least upper bound (and hence the greatest lower bound) of any two elements of the space also be in the space yields a more useful object, the vector lattice (also known as a Riesz space). Most of the common spaces encountered in analysis are of this type: the (real) continuous functions on a topological…

## 92 Citations

The constructive theory of Riesz spaces and applications in mathematical economics.

- Mathematics
- 2004

This thesis is an introduction to a constructive development of the theory of ordered vector spaces. Order structures are examined constructively; that is, with intuitionistic logic. Since the…

Common extensions for linear operators

- Mathematics
- 2011

The main meaning of the common extension for two linear operators is the following: given two vector subspaces G1 and G2 in a vector space (respectively an ordered vector space) E, a Dedekind…

INTRINSIC STRUCTURES IN AN ORDERED VECTOR SPACE

- Mathematics
- 1985

The purpose of this paper is to display intimate relationships among these intrinsic structures in an ordered vector space by putting them into suitable settings. Following a preliminary section, we…

Order Properties Of Product Spaces And Quotient Spaces Of Ordered Topological Linear Spaces

- Mathematics
- 2006

Very few we find in literature the order properties that product spaces of ordered linear spaces and ordered normed spaces carry from their component spaces. Some authors have studied certain order…

Suprema in ordered vector spaces : a constructive approach

- Mathematics
- 2007

Ordered vector spaces are examined from the point of view of Bishop’s constructive mathematics, which can be viewed as the constructive core of mathematics. Two different (but classically equivalent)…

On Products of Ordered Normed Spaces

- Mathematics

F. Riesz, H. Freudenthal, L.V. Kantorovitch, Kakutani and others initiated the study of ordered linear spaces in the late 1930’s. The theory developed into a mathematical discipline around 1950’s. It…

EXTENSION OF LINEAR OPERATORS, DISTANCED CONVEX SETS AND THE MOMENT PROBLEM

- Mathematics
- 2004

One applies an extension theorem of linear operators ((10, Theorem 5, p. 969)) to the classical moment problem in spaces of continuous functions on a compact interval and in spaces of analytic…

A sandwich theorem for functions defined on unbounded finite-simplicial sets, some inequalities and the moment problem

- Mathematics
- 2005

We recall the following sandwich-type problem: let X be a convex subset of a real vector space E, f, g : X → R two maps, g convex, f concave, g ≤ f . The problem is: in what conditions upon X, for…

On Markov Moment Problem, Polynomial Approximation on Unbounded Subsets, and Mazur-Orlicz Theorem

- MathematicsSymmetry
- 2021

A general extension theorem for linear operators with two constraints is recalled and applied to concrete spaces and found that Hahn–Banach type theorems for the extension of linear operators having a codomain such a space can be applied.

On Markov Moment Problem and Related Results

- MathematicsSymmetry
- 2021

New results and theorems on the vector-valued Markov moment problem are proved by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result.