Contribuições para as teorias linear e não-linear dos operadores somantes

Abstract

The aim of this work is to present some contributions to the theory of absolutely summing operators. In linear context, we define and study a vector-valued sequence space, called the space of anisotropic (s,q,r)-summable sequences and also we define two classes of linear operators involving this new space. Furthermore, we extend the scope of three important results in the linear theory; the first was obtained Bu and Kranz, the second one is due to Bu and the third one is due to Kwapién. Finally, now in the non-linear environment, we present an abstract approach to another famous result of S. Kwapién that relates a summing operator and its adjoint and we show that, even when restricted to the linear case, our result generalizes Kwapién’s theorem.