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Introduction to Banach Algebras, Operators, and Harmonic Analysis
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Details

  • Page extent: 336 pages
  • Size: 228 x 152 mm
  • Weight: 0.476 kg

Paperback

 (ISBN-13: 9780521535847 | ISBN-10: 0521535840)

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.

• Chapters written be leading researchers on current topics • Ideal for graduate students starting research • Carefully edited to form a coherent introduction to research

Contents

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

Review

'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

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