The extremal structure of convex sets of multilinear operators

In an article published forty years ago, Kutateladze proposed a machinery for studying the extremal structure of convex sets of linear operators which was based on the theory of Kantorovich spaces. The purpose of this article is to extend a portion of the so-arising theory to the convex sets of positive multilinear operators from the Cartesian product of vector lattices to a Kantorovich space. The approach we propose is to combine linearization by using the Fremlin tensor product of vector lattices and a recent result on factorization of lattice multimorphisms.