A propriedade de Schur em espaços de Banach

Abstract

The main purpose of this dissertation is to perform a thorough study of the Schur property in Banach spaces. We start with some basic results on Functional Analysis and General Topology that shall be useful throughout the work. In the second chapter we present several results related to the Schur property, mainly concerning characterizations of the Schur property in Banach spaces and in dual spaces. A few examples of Banach spaces with and without the Schur property and relationships of this property with some other classical properties in Banach space theory are also presented. In the third chapter we present the construction of several other outstanding spaces with the Schur property.