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Basic Classes of Linear Operators

  • Textbook
  • © 2003

Overview

Authors:
  1. Israel Gohberg

    1. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel

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  2. Seymour Goldberg

    1. Department of Mathematics, University of Maryland, College Park, USA

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  3. Marinus A. Kaashoek

    1. Department of Mathematics and Computer Science, Vrije Universiteit Amsterdam, Amsterdam, Netherlands

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  • Significantly enlarged and revised version of "Basic Operator Theory" by I. Gohberg and S. Goldberg
  • Introductory textbook for senior undergraduate or graduate courses on operator theory or functional analysis
  • Large number of examples and exercises included

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xvii
    Download chapter PDF

  2. Hilbert Spaces

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 1-50

  3. Bounded Linear Operators on Hilbert Spaces

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 51-133

  4. Laurent and Toeplitz Operators

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 135-170

  5. Spectral Theory of Compact Self Adjoint Operators

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 171-191

  6. Spectral Theory of Integral Operators

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 193-202

  7. Unbounded Operators on Hilbert Space

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 203-217

  8. Oscillations of an Elastic String

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 219-223

  9. Operational Calculus with Applications

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 225-235

  10. Solving Linear Equations by Iterative Methods

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 237-242

  11. Further Developments of the Spectral Theorem

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 243-257

  12. Banach Spaces

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 259-275

  13. Linear Operators on a Banach Space

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 277-298

  14. Compact Operators on Banach Spaces

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 299-315

  15. Poincaré Operators: Determinant and trace

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 317-345

  16. Fredholm Operators

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 347-360

  17. Toeplitz and Singular Integral Operators

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 361-399

  18. Non Linear Operators

    • Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek
    Pages 401-407

  19. Back Matter

    Pages 409-425
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Keywords

About this book

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.

Reviews

"With a name like Gohberg–Goldberg–Kaashoek, it has got to be good. But let me count the ways. If you are interested in learning the basic theories of Hilbert and Banach spaces together with the well-known operators that act on them, this book is for you. It is intended for advanced undergraduate and beginning graduate students in mathematics.... The volume is actually a second edition of Basic Operator Theory by Gohberg and Goldberg.... Exercises and examples have been added.... The text is well written, clear, and readable.... A student at the specified level will have no difficulty understanding the presentation."

—SIAM Review

 

"The material is presented in a very clear way, emphasizing concepts over technical generalities. Another pleasant feature of the book is the large number of examples and exercises. In summary, the authors have successfully found an interesting way from the elementary level to some of the highlights of operator theory."

- Monatshefte für Mathematik 

Authors and Affiliations

  • School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel

    Israel Gohberg

  • Department of Mathematics, University of Maryland, College Park, USA

    Seymour Goldberg

  • Department of Mathematics and Computer Science, Vrije Universiteit Amsterdam, Amsterdam, Netherlands

    Marinus A. Kaashoek

Bibliographic Information

  • Book Title: Basic Classes of Linear Operators

  • Authors: Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek

  • DOI: https://doi.org/10.1007/978-3-0348-7980-4

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2003

  • Softcover ISBN: 978-3-7643-6930-9Published: 24 October 2003

  • eBook ISBN: 978-3-0348-7980-4Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XVII, 423

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Operator Theory

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