Operadores extremos en espacios de Banach

Abstract

This dissertation is devoted to study a class of Banach spaces in which the class of extreme operators agree with the more restricted class called nice operators. This agreement has been previously considered in different types of Banach spaces. We fix some notation in order to give the accurate notions we are going to deal with. Only real Banach spaces will be considered in this dissertation. If X is a Banach space, then BX, SX, and EX will stand for the closed unit ball of X, the sphere of X, and the set of extreme points of BX, respectively. Given another normed space Y , we denote by L(X; Y ) the space of all continuous linear operators from X into Y endowed with its canonical norm. When Y = R, we will write X*, the dual space of X, instead of L(X;R). For T in L(X; Y ) we define T* L(Y*;X*), the adjoint operator of T, by T*(y*) = y* T for all y* in Y*. Once we have introduced the basic notation we can explain the main results of each chapter.