Dominated multilinear operators defined on tensor products of Banach spaces

Abstract

In this paper, we introduce and study new classes of dominated multilinear operators, which we call ðp; p1; . . .; pn;G1; . . .;GnÞ-dominated and ð ~ p; p1; . . .; pn;G1; . . .;GnÞ-dominated multilinear operators defined on the tensor product of Banach spaces. Some characterizations of this type of operators are given and we prove some important coincidence results. As an application, we characterize ðp; p1; . . .; pnÞ-dominated multilinear operators on CðK;GÞ and ðp; p1; . . .; pnÞdominated multilinear operators in the sense of Dinculeanu on CðK;GÞ, where K is a compact Hausdorff space and G a Banach space. We also treat the connection between an operator T and its associated operators Tt; T~ and T# for certain classes