Sobre certas relações entre classes de operadores lineares e multilineares em espaços de Banach

Abstract

The goal of this work is to present certain relations between the linear and multilinear theories of operators in Banach spaces, establishing results based on these relations. First, we present a class of mid-summing linear operators and a somewhat convenient relationship between these operators and certain classes of multiple summing multilinear operators. As a consequence, we establish inclusions and coincidence results for the presented class of linear operators. Next, we present a result, in a certain way, in the opposite direction of the previous one, with which it is possible to characterize classes of n-linear applications through the continuity of (n − 1)-linear operators. In this case we present applications of the result to bilinear operators.