A course in functional analysis and meas
β Kadets V.
π Library
π
2018
π Springer
π English
β¦ LIBER β¦
π
A Course in Functional Analysis and Measure Theory
β Scribed by Vladimir Kadets
- Publisher
- Springer International Publishing
- Year
- 2018
- Tongue
- English
- Leaves
- 553
- Series
- Universitext
- Edition
- 1st ed.
- Category
- Library
β¬ Acquire This Volume
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
β¦ Table of Contents
Front Matter ....Pages i-xxii
Metric and Topological Spaces (Vladimir Kadets)....Pages 1-32
Measure Theory (Vladimir Kadets)....Pages 33-77
Measurable Functions (Vladimir Kadets)....Pages 79-96
The Lebesgue Integral (Vladimir Kadets)....Pages 97-136
Linear Spaces, Linear Functionals, and the HahnβBanach Theorem (Vladimir Kadets)....Pages 137-158
Normed Spaces (Vladimir Kadets)....Pages 159-180
Absolute Continuity of Measures and Functions. The Connection Between Derivative and Integral (Vladimir Kadets)....Pages 181-201
The Integral on C(K) (Vladimir Kadets)....Pages 203-230
Continuous Linear Functionals (Vladimir Kadets)....Pages 231-248
Classical Theorems on Continuous Operators (Vladimir Kadets)....Pages 249-275
Elements of Spectral Theory of Operators. Compact Operators (Vladimir Kadets)....Pages 277-309
Hilbert Spaces (Vladimir Kadets)....Pages 311-341
Functions of an Operator (Vladimir Kadets)....Pages 343-370
Operators in (L_p) (Vladimir Kadets)....Pages 371-407
Fixed Point Theorems and Applications (Vladimir Kadets)....Pages 409-430
Topological Vector Spaces (Vladimir Kadets)....Pages 431-468
Elements of Duality Theory (Vladimir Kadets)....Pages 469-500
The KreinβMilman Theorem and Its Applications (Vladimir Kadets)....Pages 501-523
Back Matter ....Pages 525-539
β¦ Subjects
Mathematics; Functional Analysis; Measure and Integration; Operator Theory; Real Functions
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