Uma Introdução a Álgebras de Banach e C*- Álgebras

• Autor(a) principal: Germano, Geilson Ferreira
• Data de Publicação: 2014
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/9813
• topic: Álgebras de Banach Construção GNS,; C*-álgebras; Teorema de Gelfand-Naimark; Teorema de Gleason-Kahane-Zelazko.; Banach Algebras GNS Constrution; C*-algebras; Gelfand-Naimark Theorem; Gleason-Kahane-Zelazko Theorem; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this dissertation we develop a rst contact with the theory of Banach Algebras and C*-algebras. As usual of a rst contact, we build the Spectral Theory in Banach algebras with unit. We present the characterization theorems of C *-algebras of Gelfand-Naimark and Gelfand-Naimark-Segal, including the GNS construction. Moreover, we prove a theorem which characterizes all complex homomorphisms in the C*-algebra C(X), as point-evaluation homomorphisms. We also present, as a curiosity, a proof of the Fundamental Theorem of Algebra using the Gelfand-Mazur Theorem. As a prerequisite to the Gelfand-Naimark-Segal's characterization of C *-algebras, we further develop, in the background, the theory of the direct sum of any family of Hilbert spaces. .