Synopses & Reviews
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.
Includes bibliographical references (p. 316-317) and indexes.
Based on lectures given at an instructional course, this volume enables readers with a basic knowledge of functional analysis to access key research in the field. The authors survey several areas of current interest, making this volume ideal preparatory reading for students embarking on graduate work as well as for mathematicians working in related areas.
Arising from lecture courses given by the authors, this book gives introductions to important topics in functional analysis at a level ideal for beginning graduate students as well as others interested in the subject. The collection is carefully written to form a coherent and accessible introduction to current research topics.
Introduction to important topics in functional analysis from leading researchers. Ideal for graduate students.
Table of Contents
1. Banach algebras; 2. Harmonic analysis and amenability; 3. Invariant subspaces; 4. Local spectral theory; 5. Single-valued extension property and Fredholm theory.