Análise funcional e algumas aplicações

Abstract

The theory of functional analysis is a branch of mathematics that originated from classical analysis and its development helped to solve problems of different fields of mathematics. In the first part of this work we address the central concepts of this theory, Banach spaces, which are complete normed vector spaces, and Hilbert spaces that are Banach spaces with an internal product. And we present examples of these spaces and some results that involve these concepts. In the second part of the paper, we present the most important theorems of functional analysis, which are Hahn-Banach’s theorem, closed-graph theorem, Banach fixed-point theorem, BanachSteinhaus theorem and open application theorem. In addition, we make an application of each of these theorems.