Produto tensorial entre espaços de Banach e aplicações

Abstract

This work has as the main purpose to study the tensor product between Banach spaces. For this, initially, we will present some results of Functional Analysis and of vector-valued sequence spaces that will be necessary to the development of the later contents. Next, we will make an algebraic study of the tensor product of vector spaces, highlighting its construction and its properties. In the topological bias, we will study the projective and injective norms, their properties and the dual of the projective tensor product. Finally, we will see two applications of the tensor product between Banach spaces, namely one with respect to the composition method, which generates multi-ideals from the linear operator ideals, and other related to a characterization for the absolutely summing operators.