A Course in Commutative Banach Algebras

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 Requiring only a basic knowledge of functional analysis, topology, complex analysis, measure theory and group theory, this book provides a thorough and self-contained introduction to the theory of commutative Banach algebras. The core are 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 aims at graduate students and can be used as a text for courses on Banach algebras, with various possible specializations, or a Gelfand theory based course in harmonic analysis.