Homogeneous Polynomials: Harmonic Means and Completely Partitioned Weighted Geometric Means

TL;DR

This paper introduces new characterizations of bounded orthogonally additive polynomials in vector lattices using harmonic and weighted geometric means, generalizing recent theorems in the field.

Contribution

It provides novel characterizations of these polynomials via harmonic and partitioned weighted geometric means, extending previous results by Kusraeva and others.

Findings

New characterizations of bounded orthogonally additive polynomials

Generalization of Kusraeva's theorem on weighted geometric means

Extension of related theorems in vector lattice theory

Abstract

We provide two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into a convex bornological space using harmonic means and completely partitioned weighted geometric means. Our result involving completely partitioned weighted geometric means generalizes a recent theorem on bounded orthogonally additive polynomials by Z.A. Kusraeva as well as parts of related theorems by G. Buskes and the author.