Monomial decomposition of homogeneous polynomials in vector lattices

Abstract

‎ ‎The paper is devoted to the characterization and weighted shift representation of regular homogeneous polynomials between vector lattices admitting a decomposition into a sum of monomials in lattice homomorphisms‎. ‎The main tool is the factorization theorem for order bounded disjointness preserving multilinear operators obtained earlier by the authors‎.