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A course in functional analysis and measure theory

Author: V M Kadet︠s︡; A Iacob
Publisher: Cham, Switzerland : Springer, 2018.
Series: Universitext
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Kadet︠s︡, V. M. (Vladimir M.).
Course in functional analysis and measure theory.
Cham, Switzerland : Springer, 2018
(OCoLC)1032030203
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: V M Kadet︠s︡; A Iacob
ISBN: 9783319920047 3319920049
OCLC Number: 1045425109
Description: 1 online resource (xxii, 539 pages)
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.
Series Title: Universitext
Responsibility: Vladimir Kadets ; translated from the Russian by Andrei Iacob.

Abstract:

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.

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"'This is a capital textbook of functional analysis, measure theory and operator theory, excellently written by an experienced author. The book is based on undergraduate courses of functional Read more...

 
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