Kadets V.A Course in Functional Analysis and Measure Theory

Springer, 2018. — 553 p. — (Universitext). — ISBN: 3319920030.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 covers measure and integration theory, classical Banach and Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases, the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity theory.
Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis. Including over 1500 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses.Metric and Topological Spaces
Measure Theory
Measurable Functions
The Lebesgue Integral
Linear Spaces, Linear Functionals, and the Hahn–Banach Theorem
Normed Spaces
Absolute Continuity of Measures and Functions. The Connection Between Derivative and Integral
The Integral on C(K)
Continuous Linear Functionals
Classical Theorems on Continuous Operators
Kadets, Vladimir
Elements of Spectral Theory of Operators. Compact Operators
Hilbert Spaces
Functions of an Operator
Operators in Lp
Fixed Point Theorems and Applications
Topological Vector Spaces
Elements of Duality Theory
The Krein–Milman Theorem and Its Applications