Regularity of Continuous Multilinear Operators and Homogeneous Polynomials

Regular multilinear operators and regular homogeneous polynomials acting between Banach lattices are automatically continuous, but the converse, in general, is not true. The problem arises of characterizing Banach lattices for which the classes of continuous and regular multilinear operators (or homogeneous polynomials) coincide. The aim of this note is to extend two results in this direction, earlier obtained for linear operators, to the above-mentioned classes of operators and polynomials. The main method is linearization with the use of the Fremlin tensor product of Banach lattices.