This book provides a thorough and self-contained introduction to the theory of commutative Banach algebras, aimed at graduate students with a basic knowledge of functional analysis, topology, complex analysis, measure theory, and group theory. At the core of this text are the chapters on Gelfand's theory, regularity and spectral synthesis. Special emphasis is placed on applications in abstract harmonic analysis and on treating many special classes of commutative Banach algebras, such as uniform algebras, group algebras and Beurling algebras, and tensor products. Detailed proofs and a variety of exercises are given. The book is intended for graduate students taking a course on Banach algebras,with various possible specializations, or a Gelfand theory based course in harmonic analysis. Author has carefully chosen the most important topics within Banach algebra theory Incorporates recent advances concerning so-called spectral extension properties and the unique uniform norm property Investigates projective tensor products under all aspects of the book Exercises are plentiful throughout the text Class-tested at the University of Heidelberg, Technical University of Munich, and University of Paderborn INDICE: Preface.- General Theory of Banach Algebras.- Gelfand Theory.- Functional Calculus, Shilov Boundary, and Applications.- Regularity and Related Properties.- Spectral Synthesis and Ideal Theory.- Appendix.- References.- Index.
- ISBN: 978-0-387-72475-1
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 370
- Fecha Publicación: 01/12/2008
- Nº Volúmenes: 1
- Idioma: Inglés