Characterizing Bounded Orthogonally Additive Polynomials on Vector Lattices

TL;DR

This paper provides new formulas to characterize bounded orthogonally additive polynomials on vector lattices, enhancing understanding through both existing and novel approaches involving complexification.

Contribution

It introduces new characterizing formulas for bounded orthogonally additive polynomials using complexification techniques, building on and extending previous results.

Findings

Formulas that characterize orthogonally additive polynomials are validated.

New characterizations are derived via complexification methods.

The work clarifies the structure of these polynomials in vector lattices.

Abstract

We derive formulas for characterizing bounded orthogonally additive polynomials in two ways. Firstly, we prove that certain formulas for orthogonally additive polynomials derived in \cite{Kusa} actually characterize them. Secondly, by employing complexifications of the unique symmetric multilinear maps associated with orthogonally additive maps we derive new characterizing formulas.