The present book is an expanded and enriched version ofthe textBasicOperator Theory, written by the first two authors more than twenty years ago. Since then the three ofus have used the basic operator theory text in various courses. This experience motivated us to update and improve the old text by including a wider variety ofbasic classes ofoperators and their applications. The present book has also been written in such a way that it can serve as an introduction to our previous booksClassesofLinearOperators, Volumes I and II. We view the three books as a unit. We gratefully acknowledge the support of the mathematical departments of Tel-Aviv University, the University of Maryland at College Park, and the Vrije Universiteit atAmsterdam. The generous support ofthe Silver Family Foundation is highly appreciated. Amsterdam, November 2002 The authors Introduction This elementary text is an introduction to functional analysis, with a strong emphasis on operator theory and its applications. It is designed for graduate and senior undergraduate students in mathematics, science, engineering, and other fields
CONTENT
Introduction -- Hilbert Spaces -- Bounded Linear Operators on Hilbert Spaces -- Laurent and Toeplitz Operators on Hilbert Spaces -- Spectral Theory of Compact Self-Adjoint Operators -- Spectral Theory of Integral Operators -- Unbounded Operators on Hilbert Spaces -- Oscillations of an Elastic String -- Operational Calculus with Applications -- Solving Linear Equations by Iterative Methods -- Further Developments of the Spectral Theorem -- Banach Spaces -- Linear Operators Banach Spaces -- Compact Operators on Banach Spaces -- Poincarรฉ Operators: Determinant and Trace -- Fredholm Operators -- Toeplitz and Singular Integral Operators -- Nonlinear Operators
