Introduction to Banach Algebras, Operators, and Harmonic Analysis

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H. Garth Dales (University of Leeds) Pietro Aiena (Università degli Studi, Palermo, Italy)

Introduction to Banach Algebras, Operators, and Harmonic Analysis

H. Garth Dales (University of Leeds), Pietro Aiena (Università degli Studi, Palermo, Italy), Jörg Eschmeier (Universität des Saarlandes, Saarbrücken, Germany) , Kjeld Laursen (University of Copenhagen)

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English

Cambridge University Press
13 November 2003

Functional analysis & transforms

Series: London Mathematical Society Student Texts

This work has arisen from lecture courses given by the authors on important topics within functional analysis. The authors, who are all leading researchers, give introductions to their subjects at a level ideal for beginning graduate students, and others interested in the subject. The collection has been carefully edited so as to form a coherent and accessible introduction to current research topics. The first chapter by Professor Dales introduces the general theory of Banach algebras, which serves as a background to the remaining material. Dr Willis then studies a centrally important Banach algebra, the group algebra of a locally compact group. The remaining chapters are devoted to Banach algebras of operators on Banach spaces: Professor Eschmeier gives all the background for the exciting topic of invariant subspaces of operators, and discusses some key open problems; Dr Laursen and Professor Aiena discuss local spectral theory for operators, leading into Fredholm theory.

By: H. Garth Dales (University of Leeds), Pietro Aiena (Università degli Studi, Palermo, Italy), Jörg Eschmeier (Universität des Saarlandes, Saarbrücken, Germany), Kjeld Laursen (University of Copenhagen), George A. Willis (University of Newcastle, New South Wales)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 57
Dimensions: Height: 235mm, Width: 159mm, Spine: 23mm
Weight: 600g
ISBN: 9780521828932
ISBN 10: 0521828937
Series: London Mathematical Society Student Texts
Pages: 336
Publication Date: 13 November 2003
Audience: Professional and scholarly , Undergraduate
Replaced By: 9780521535847
Format: Hardback
Publisher's Status: Active

1. Banach algebras; 2. Harmonic analysis and amenability; 3. Invariant subspaces; 4. Local spectral theory; 5. Single-valued extension property and Fredholm theory.

Reviews for Introduction to Banach Algebras, Operators, and Harmonic Analysis

'In view of the book's genesis, it is clear that it is quite heterogeneous ... This heterogeneity, however, turns out to be one of the volume's strengths: it presents five concise introductions to important parts of functional analysis, each of which conveys its author's outlook on the field ... It will certainly be quite useful for new graduate students as well as for non-specialists in the areas covered who want to get a quick overview before delving into dautingly thick treatises as the one by [H. G. Dales ['Banach algebras and automatic continuity', Lond. Math. Soc. Monographs. New Series 24 (2000; Zbl 981.46043)] (on Banach algebras) or K. B. Laursen and M. M. Neumann ...'. Zentralblatt MATH