Normas tensoriais do tipo injetiva, propriedade de Dunford-Pettis e espaçabilidade no ambiente de classes de sequências

Abstract

In this work, we develop and expand the scope of the abstract environment based on the concept of sequence classes in three directions: in the theory of tensor norms and integral-type bilinear forms, in the direction of Dunford-Pettis type properties, and in the direction of spaceability in the context of sequence spaces and classes of linear operators. In the first part of the work, we study some classes of injective-type norms for the tensor product and the duality of these spaces, from which arises the definition of an integral-type bilinear form and a characterization for a certain sequence space. We also define and study a new concept of sequence class, called B-class, and present a generalization of the Dunford-Pettis property to Banach spaces. In the second part, we define and study the concept of standard sequence class, inspired by the concept of sequence class, with which we investigate notions of spaceability in the environments of (differences between) quasi-Banach sequence spaces and classes of linear operators.