Uma introdução à análise funcional e à equação de daugavet

Abstract

This work aims to study topics in Functional Analysis and results about the Daugavet equation. For this purpose, we will start by reviewing some issues of General Topology and Measure Theory. In the sequence, we will perform a study in Functional Analysis, where we will investigate the basic theory of continuous linear operators between normed and Banach spaces; the classical theorems of Hahn-Banach and Banach-Steinhaus, the Open Mapping Theorem and the Closed Graph Theorem. Finally, we will present some relevant results about the Daugavet equation.