O adjunto de um polinômio homogêneo contínuo entre espaços de Banach

Abstract

The main purpose of this dissertation is the study of the adjoint of a continuous homogeneous polynomial between Banach spaces. First we prove some basic properties and provide some examples of adjoints of certain homogeneous polynomials. Next we study the adjoint of the compositions u◦P and P◦u, where P is a homogeneous polynomial and u is a linear operator, both of them continuous. In the last chapter we study the adjoints of some special classes of homogeneous polynomials, namely, polynomials of finite rank, approximable, compact and weakly compact. To accomplish this task we study the linearization of homogeneous polynomials through the projective symmetric tensor product and also some introductory aspects of the theory of operator ideals.