Um passeio pela análise funcional

Abstract

Functional analysis plays an increasingly important role in the applied sciences, as well as in pure mathematics itself. Consequently, it is increasingly desirable to introduce the student to this branch of mathematics at an early stage of study. Conceived as an introduction to Functional Analysis for the final student of the undergraduate degree in mathematics, this work aims to introduce the Banach and Hilbert Spaces, their consequences and results, both for finite and infinite dimensions, which is the main objective of Functional Analysis. As a final result, the last chapter of this work presents four of the main theorems of Functional Analysis, namely the Riesz Representation Theorem, the Open Application Theorem, the Closed Graph Theorem and finally, the Hahn-Banach Theorem.