O Teorema de Banach-Steinhaus e algumas consequências

Abstract

The objective of this study is to state and demonstrate, with the assistance of already established mathematical literature, one of the main theorems in functional analysis-a branch of mathematical analysis-namely the Banach-Steinhaus Theorem. This theorem is also commonly referred as the Uniform Boundedness Principle, and its main trait is to ensure a condition of uniformity over a certain class of functions. More specifically, when considering a family of continuous linear operators that are pointwise bounded within the setting of Banach spaces, this pointwise boundedness becomes uniform.