Espaços Vetoriais Normados e o Teorema da Representação de Riesz

Abstract

This work aims to present the concepts and results of normed vector space, normed vector space with inner product space, particularly Hilbert Space, and the Riesz Representation Theorem for this space, all this is analyzed through the algebraic perspective. Being a literally research, this work begins revisiting basic concepts of linear algebra and other concepts necessary for its development. After that, it is presented one of the central concepts of this work which is normed vector space, as well as some of its properties and the explanation of the Riesz Representation Theorem for the finite dimensional vector space. Finally, it is defined some necessary topological concepts for the definition of the normed vector space with inner product space application which is the Hilbert Space, ending with the Riesz Representation Theorem for this space, begin this theorem very important within the studies of Functional Analysis.