A Course in Commutative Banach Algebras

  • Eberhard Kaniuth

Part of the Graduate Texts in Mathematics book series (GTM, volume 246)

Table of contents

  1. Front Matter
    Pages 1-10
  2. Eberhard Kaniuth
    Pages 1-42
  3. Eberhard Kaniuth
    Pages 1-96
  4. Eberhard Kaniuth
    Pages 1-60
  5. Eberhard Kaniuth
    Pages 1-66
  6. Back Matter
    Pages 1-34

About this book


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.


Group theory abstract harmonic analysis algebra functional analysis harmonic analysis

Authors and affiliations

  • Eberhard Kaniuth
    • 1
  1. 1.FB 17 - Mathemathik/InformatikUniversität PaderbornPaderbornGermany

Bibliographic information