Linearização de aplicações multilineares contínuas entre espaços de Banach e multi-ideais de composição

Abstract

The rst aim of this dissertation is to construct the tensor product of nitely many linear spaces from elementary tensors and to show that this is the space through which multilinear mappings can be linearized. Next continuous multilinear mappings between Banach spaces are studied. The projective norm is introduced in the tensor product in order to perform the linearization of continuous multilinear mappings. The last chapter is devoted to the study of operator ideals and their generalization to the multilinear setting. The interplay between the theory of multi-ideals and the projective tensor product is established by the theory of composition multi-ideals.