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Functional Analysis: An Introduction

About this Title

Yuli Eidelman, Tel Aviv University, Tel Aviv, Israel, Vitali Milman, Tel Aviv University, Tel Aviv, Israel and Antonis Tsolomitis, University of the Aegean, Samos, Greece

Publication: Graduate Studies in Mathematics
Publication Year: 2004; Volume 66
ISBNs: 978-0-8218-3646-0 (print); 978-1-4704-1150-3 (online)
DOI: https://doi.org/10.1090/gsm/066
MathSciNet review: MR2067694
MSC: Primary 46-01; Secondary 47-01

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Table of Contents

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Front/Back Matter

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Part I. Hilbert spaces and basic operator theory

• 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

Part II. Basics of functional analysis

• 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 $H$
• Appendix. Solutions to exercises