O Teorema de Hahn Banach

Abstract

This work consists of the study of one of the most important theorems of Functional Analysis, the Hahn-Banach Theorem. Here, in addition to approaching the theorem in its classic versions found in the Introduction to Functional Analysis books, the analytical form and the geometric form, we will also see alternative ways to prove it, as well as equivalent results. We will approach its origin presenting its rudimentary version. Furthermore, as an illustration, we will see numerous applications of the Hahn-Banach Theorem in approaches that are the foundation in the development of the theory of Functional Analysis.