PRODUCT FACTORABLE MULTILINEAR OPERATORS DEFINED ON SEQUENCE SPACES

Abstract

We prove a factorization theorem for multilinear operators acting in topological products of spaces of (scalar) p-summable sequences through a product. It is shown that this class of multilinear operators called product fac− torable maps coincides with the well-known class of the zero product preserving operators. Due to the factorization, we obtain compactness and summability properties by using classical functional analysis tools. Besides, we give some isomorphisms between spaces of linear and multilinear operators, and repre- sentations of some classes of multilinear maps as n-homogeneous orthogonally additive polynomials.