Basic Operator Theory

By: Israel Gohberg, Seymour Goldberg

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Paperback | 1 August 2001

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304 Pages

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rii application of linear operators on a Hilbert space. We begin with a chapter on the geometry of Hilbert space and then proceed to the spectral theory of compact self adjoint operators; operational calculus is next presented as a nat ural outgrowth of the spectral theory. The second part of the text concentrates on Banach spaces and linear operators acting on these spaces. It includes, for example, the three 'basic principles of linear analysis and the Riesz Fredholm theory of compact operators. Both parts contain plenty of applications. All chapters deal exclusively with linear problems, except for the last chapter which is an introduction to the theory of nonlinear operators. In addition to the standard topics in functional anal ysis, we have presented relatively recent results which appear, for example, in Chapter VII. In general, in writ ing this book, the authors were strongly influenced by re cent developments in operator theory which affected the choice of topics, proofs and exercises. One of the main features of this book is the large number of new exercises chosen to expand the reader's com prehension of the material, and to train him or her in the use of it. In the beginning portion of the book we offer a large selection of computational exercises; later, the proportion of exercises dealing with theoretical questions increases. We have, however, omitted exercises after Chap ters V, VII and XII due to the specialized nature of the subject matter.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Probability & Statistics Applied Mathematics Differential Calculus & Equations Engineering & Technology Technology in General Engineering in General

Introduction
Hilbert Spaces
Bounded Linear Operators on Hilbert Spaces
Spectral Theory of Compact Self Adjoint Operators
Spectral Theory of Integral Operators
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 on a Banach Space
Compact Operators on a Banach Space
Non-Linear Operators
Appendix 1. Countable Sets and Separable Hilbert Spaces
Appendix 2. Lebesgue Integration and LP Spaces
Appendix 3. Proof of the Hahn-Banach Theorem
Appendix 4. Proof of the Closed Graph Theorem
Suggested Reading
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Basic Operator Theory

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