Functional Analysis An Introduction 66

This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators. The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially self-contained. Prerequisites for the first part are minimal amounts of linear algebra and calculus. For the second part, some knowledge of topology and measure theory is recommended. Each of the 11 chapters is followed by numerous exercises, with solutions given at the end of the book. The text is ideal for a one-year course. It will also provide a sound basis for further study. It is suitable for graduate students and researchers interested in operator theory and functional analysis. The goal of this textbook is to provide an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators. The text corresponds to material for two semester courses (Part I and Part II, respectively), and it is as self-contained as possible. The only prerequisites for the first part are minimal amounts of linear algebra and calculus. However, for the second course (Part II), it is useful to have some knowledge of topology and measure theory. Each chapter is followed by numerous exercises, whose solutions are given at the end of the book. Chapter 1. Linear Spaces; Normed Spaces; First Examples Chapter 2. Hilbert Spaces Chapter 3. The Dual Space Chapter 4. Bounded Linear Operators Chapter 5. Spectrum. Fredholm Theory Of Compact Operators Chapter 6. Self-adjoint Operators Chapter 7. Functions Of Operators; Spectral Decomposition Chapter 8. Spectral Theory Of Unitary Operators Chapter 9. The Fundamental Theorems And The Basic Methods Chapter 10. Banach Algebras Chapter 11. Unbounded Self-adjoint And Symmetric Operators In $h Tappendix. Solutions To Exercises Yuli Eidelman, Vitali Milman, Antonis Tsolomitis. Includes Bibliographical References (p. 311-312) And Indexes. "The goal of this textbook is to provide an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators."--BOOK JACKET Introduces the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators and spectral theory of self-adjoint operators. This work presents the theorems and methods of abstract functional analysis and applications of these methods to Banach algebras and theory of unbounded self-adjoint operators