DISJOINTNESS PRESERVING OPERATORS: DECOMPOSITION AND FACTORIZATION

The paper presents a review of the author’s recent results on the structure of order bounded disjointness preserving linear and multilinear operators, as well as homogeneous polynomials. The main attention is paid to operators that are decomposable into a sum of disjointness preserving operators and homogeneous polynomials that can be represented as a sum of operator monomials, i.e., of products of powers of disjointness preserving linear operators.