A Course in Functional Analysis and Measure Theory

• Main Author: Kadets, Vladimir (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Universitext,
• Subjects: Functional analysis.; Measure theory.; Operator theory.; Functions of real variables.; Functional Analysis.; Measure and Integration.; Operator Theory.; Real Functions.

Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis. Starting from basic topics before proceeding to more advanced material, the book...

Table of Contents:

• Introduction
• Chapter 1. Metric and topological spaces
• Chapter 2. Measure theory
• Chapter 3. Measurable functions
• Chapter 4. The Lebesgue integral
• Chapter 5. Linear spaces, linear functionals, and the Hahn-Banach theorem
• Chapter 6. Normed spaces
• Chapter 7. Absolute continuity of measures and functions. Connection between derivative and integral
• Chapter 8. The integral on C(K)
• Chapter 9. Continuous linear functionals
• Chapter 10. Classical theorems on continuous operators
• Chapter 11. Elements of spectral theory of operators. Compact operators
• Chapter 12. Hilbert spaces
• Chapter 13. Functions of an operator
• Chapter 14. Operators in Lp
• Chapter 15. Fixed-point theorems and applications
• Chapter 16. Topological vector spaces
• Chapter 17. Elements of duality theory
• Chapter 18. The Krein-Milman theorem and applications
• References. Index.