Invertibility and Singularity for Bounded Linear Operators

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.

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.

ProloguePreface1. Normed Linear Spaces2. Bounded Linear Operators3. Invertibility and Singularity4. Banach Spaces and Completeness5. Linear Functions and Duality6. Finite Dimensional Spaces and Compactness7. Operator Algebra nand Commutivity8. Inner Products and Orthogonality9. Liouville's Theorem and Spectral Theory10. Comparisons of Operators and Exactness11. Multiparameter Spectral TheoryEpilogueNotes, Comments, and ExercisesReferencesNotationIndex