Contribuições à teoria dos operadores Cohen fortemente somantes.

Abstract

This work presents a study of Cohen the strongly summing operators from the point of view of the theory of ideas of operators and polynomials. Furthermore, we introduce two new classes of operators that generalize the concept of multilinear operators and polynomials of this nature, namely, the multiple strongly summing Cohen operators and the strongly summing Cohen operators at a given point. We show that the new defined classes, like the previous ones, form normed operator/polynomial ideals and that the strongly summing multiple Cohen operators form a Banach ideal. We also show that the construction of the strongly summing Cohen multiple operator class provides a kind of holomorphy and a coherent and compatible sequence of ideas.