A Course in Commutative Banach Algebras

Eberhard Kaniuth

ISBN 10: 1441924795 / ISBN 13: 9781441924797

Published by Springer US, Springer New York Nov 2010, 2010

About this Item

Neuware -Banach algebras are Banach spaces equipped with a continuous multipli- tion. In roughterms,there arethree types ofthem:algebrasofboundedlinear operators on Banach spaces with composition and the operator norm, al- bras consisting of bounded continuous functions on topological spaces with pointwise product and the uniform norm, and algebrasof integrable functions on locally compact groups with convolution as multiplication. These all play a key role in modern analysis. Much of operator theory is best approached from a Banach algebra point of view and many questions in complex analysis (such as approximation by polynomials or rational functions in speci c - mains) are best understood within the framework of Banach algebras. Also, the study of a locally compact Abelian group is closely related to the study 1 of the group algebra L (G). There exist a rich literature and excellent texts on each single class of Banach algebras, notably on uniform algebras and on operator algebras. This work is intended as a textbook which provides a thorough introduction to the theory of commutative Banach algebras and stresses the applications to commutative harmonic analysis while also touching on uniform algebras. In this sense and purpose the book resembles Larsen¿s classical text [75] which shares many themes and has been a valuable resource. However, for advanced graduate students and researchers I have covered several topics which have not been published in books before, including some journal articles.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 368 pp. Englisch.

Seller Inventory # 9781441924797

Bibliographic Details

• Title: A Course in Commutative Banach Algebras
• Publisher: Springer US, Springer New York Nov 2010
• Publication Date: 2010
• Language: English
• ISBN 10: 1441924795
• ISBN 13: 9781441924797
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

This book provides a thorough and self-contained introduction to the theory of commutative Banach algebras. The author has carefully chosen the most important topics within Banach algebra 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.

From the Back Cover

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.