Uma Introdução a Álgebras de Banach e C*- Álgebras - Germano, Geilson Ferreira (2014)
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. .