Convolution-factorable multilinear operators

Abstract

We study multilinear operators defined on topological products of Banach algebras of integrable functions and Banach left modules with con-volution product. The main theorem of the paper presents a factorization for multilinear operators through convolution that implies the property known as zero product preservation. By using this factorization we investigate prop-erties of multilinear operators including integral representations and we give applications related to orthogonally additive homogeneous polynomials and Hilbert-Schmidt operators.