Polynomial Valuations on Vector Lattices

TL;DR

This paper establishes a fundamental link between polynomial valuations and orthosymmetric multilinear maps on vector lattices, providing a concise proof of their equivalence to orthogonal additivity.

Contribution

It demonstrates that polynomial valuations correspond to orthosymmetric multilinear maps, clarifying their structure and relationship to orthogonal additivity in vector lattices.

Findings

Polynomial valuations correspond to orthosymmetric multilinear maps.

Orthosymmetry is equivalent to orthogonal additivity.

Provides a concise proof of this equivalence.

Abstract

We prove that polynomial valuations on vector lattices correspond to orthosymmetric multilinear maps. As a consequence we obtain a concise proof of the equivalence of orthosymmetry and orthogonal additivity.