Factorization of multilinear operators defined on products of function spaces - ERDOĞAN, EZGİ (TAYLOR & FRANCIS LTD, 2022)
This paper deals with multilinear operators acting in products of Banach spaces that factor through a canonical mapping. We prove some factorization theorems and characterizations by means of norm inequalities for multilinear operators defined on the n-fold Cartesian product of the space of bounded Borel measurable functions, respectively, products of Banach function spaces. These factorizations allow us to obtain integral dominations and lattice geometric properties and to present integral representations for abstract classes of multilinear operators. Finally, bringing together these ideas, some applications are shown, regarding for example summability properties and representation of multilinear maps as orthogonally additive n-homogeneous polynomials.
Keywords: Multilinear and polynomial operators; Banach function spaces; factorization; zero product preservation; symmetric operator; ORTHOGONALLY ADDITIVE POLYNOMIALS; BILINEAR OPERATORS; F-ALGEBRAS; FACTORABILITY; THEOREM; MAPS