This introduction to functional analysis focuses on the types of singularity that prevent an operator from being invertible. The presentation is based on the open mapping theorem, Hahn-Banach theorem, dual space construction, enlargement of normed space, and Liouville's theorem. Suitable for advanced undergraduate and graduate courses in functional analysis, this volume is also a valuable resource for researchers in Fredholm theory, Banach algebras, and multiparameter spectral theory.
The treatment develops the theory of open and almost open operators between incomplete spaces. It builds the enlargement of a normed space and of a bounded operator and sets up an elementary algebraic framework for Fredholm theory. The approach extends from the definition of a normed space to the fringe of modern multiparameter spectral theory and concludes with a discussion of the varieties of joint spectrum. This edition contains a brief new Prologue by author Robin Harte as well as his lengthy new Epilogue, "Residual Quotients and the Taylor Spectrum."
Dover republication of the edition published by Marcel Dekker, Inc., New York, 1988.
About the Author
Robin Harte received his PhD from the University of Cambridge and taught at the University Colleges of Swansea and Cork in addition to visiting the universities of Iowa, Fairbanks, Lille, and Mexico. He remains loosely affiliated with Trinity College, Dublin, and is the author of Spectral Mapping Theorems: A Bluffer's Guide.
Table of Contents
1. Normed Linear Spaces
2. Bounded Linear Operators
3. Invertibility and Singularity
4. Banach Spaces and Completeness
5. Linear Functions and Duality
6. Finite Dimensional Spaces and Compactness
7. Operator Algebra nand Commutivity
8. Inner Products and Orthogonality
9. Liouville's Theorem and Spectral Theory
10. Comparisons of Operators and Exactness
11. Multiparameter Spectral Theory
Notes, Comments, and Exercises