Ebook: Basic Classes of Linear Operators

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.

---

This book provides an introduction to functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis. As textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and proceeds to the theory of linear operators on these spaces including Banach spaces. Presented as a natural continuation of linear algebra, the book provides a firm foundation in operator theory which is an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.

Enriched new version of the book "Basic Operator Theory" by I. Gohberg and S. Goldberg (ISBN 0-8176-4262-5).

---

This book provides an introduction to functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis. As textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and proceeds to the theory of linear operators on these spaces including Banach spaces. Presented as a natural continuation of linear algebra, the book provides a firm foundation in operator theory which is an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.

Enriched new version of the book "Basic Operator Theory" by I. Gohberg and S. Goldberg (ISBN 0-8176-4262-5).

Content:
Front Matter....Pages i-xvii
Hilbert Spaces....Pages 1-50
Bounded Linear Operators on Hilbert Spaces....Pages 51-133
Laurent and Toeplitz Operators....Pages 135-170
Spectral Theory of Compact Self Adjoint Operators....Pages 171-191
Spectral Theory of Integral Operators....Pages 193-202
Unbounded Operators on Hilbert Space....Pages 203-217
Oscillations of an Elastic String....Pages 219-223
Operational Calculus with Applications....Pages 225-235
Solving Linear Equations by Iterative Methods....Pages 237-242
Further Developments of the Spectral Theorem....Pages 243-257
Banach Spaces....Pages 259-275
Linear Operators on a Banach Space....Pages 277-298
Compact Operators on Banach Spaces....Pages 299-315
Poincar? Operators: Determinant and trace....Pages 317-345
Fredholm Operators....Pages 347-360
Toeplitz and Singular Integral Operators....Pages 361-399
Non Linear Operators....Pages 401-407
Back Matter....Pages 409-425

---

This book provides an introduction to functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis. As textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and proceeds to the theory of linear operators on these spaces including Banach spaces. Presented as a natural continuation of linear algebra, the book provides a firm foundation in operator theory which is an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.

Enriched new version of the book "Basic Operator Theory" by I. Gohberg and S. Goldberg (ISBN 0-8176-4262-5).

Content:
Front Matter....Pages i-xvii
Hilbert Spaces....Pages 1-50
Bounded Linear Operators on Hilbert Spaces....Pages 51-133
Laurent and Toeplitz Operators....Pages 135-170
Spectral Theory of Compact Self Adjoint Operators....Pages 171-191
Spectral Theory of Integral Operators....Pages 193-202
Unbounded Operators on Hilbert Space....Pages 203-217
Oscillations of an Elastic String....Pages 219-223
Operational Calculus with Applications....Pages 225-235
Solving Linear Equations by Iterative Methods....Pages 237-242
Further Developments of the Spectral Theorem....Pages 243-257
Banach Spaces....Pages 259-275
Linear Operators on a Banach Space....Pages 277-298
Compact Operators on Banach Spaces....Pages 299-315
Poincar? Operators: Determinant and trace....Pages 317-345
Fredholm Operators....Pages 347-360
Toeplitz and Singular Integral Operators....Pages 361-399
Non Linear Operators....Pages 401-407
Back Matter....Pages 409-425
....