Positive Polynomials on Riesz Spaces

TL;DR

This paper explores properties of positive polynomial mappings in Riesz spaces, establishing analogues of classical linearity and extension theorems using finite difference calculus.

Contribution

It introduces polynomial analogues of classical theorems for positive, additive mappings in Riesz spaces, expanding the theoretical framework.

Findings

Positive polynomial mappings are characterized using finite difference calculus.

A polynomial version of the classical result that positive, additive mappings are linear is proved.

A polynomial extension theorem analogous to Kantorovich's is established.

Abstract

We prove some properties of positive polynomial mappings between Riesz spaces, using finite difference calculus. We establish the polynomial analogue of the classical result that positive, additive mappings are linear. And we prove a polynomial version of the Kantorovich extension theorem.