Operator Algebras were originally introduced by F. Riesz, J. von Neumann, I. Gelfand and M. Naimark. This area became particularly relevant at the end of the 20th century and still remains a very active research area. Two Fields medals were awarded in this field to Alain Connes, in 1982, and Vaughan Jones, in 1990.
The main goal of this book is to present an introduction to the theory of Operator Algebras covering the main topics in the area. The book consists of 6 chapters entitled: “Teoria espectral em álgebras de Banach” (Spectral Theory and Banach Algebras), “Representações de álgebras de Banach” (Representations of Banach algebras), “Fundamentos de álgebras C*” (Fundamentals of C * algebras), “Representações e classes de álgebras C*” (Representations and classes of C * algebras), “Sistemas Dinâmicos e produtos cruzados C*” (C* dynamical systems and crossed product) and “Introdução às Álgebras de von Neumann” (Introduction to von Neumann algebras).
Operator Algebras is an important branch of Functional Analysis with links to other areas of mathematics, namely Operator Theory, Dynamical Systems, Noncommutative Geometry, Probability Theory, Numerical Analysis, as well as Mathematical Physics.
The book is available at IST press online store, and will be available soon at libraries: Almedina, Bertrand, Fnac, Wook, etc.