Convolution-factorable multilinear operators

Abstract

We study multilinear operators defined on topological products of Banach algebras of integrable functions and Banach left modules with convolution 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 properties of multilinear operators including integral representations and we give applications related to orthogonally additive homogeneous polynomials and Hilbert-Schmidt operators.2020 Mathematics Subject Classification. 47H60, 47A68.