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Functional Analysis

An Introductory Course

Author(s):
Publisher:

Springer

Pages: 205
Further Actions:

Recommend to library

AVAILABLE FORMATS

Paperback - 9783319915111

29 June 2018

$54.99

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Ebook - 9783319915128

09 June 2018

$39.99

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This concise text provides a gentle introduction to functional analysis. Chapters cover essential topics such as special spaces, normed spaces, linear functionals, and Hilbert spaces. Numerous examples and counterexamples...

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This concise text provides a gentle introduction to functional analysis. Chapters cover essential topics such as special spaces, normed spaces, linear functionals, and Hilbert spaces. Numerous examples and counterexamples aid in the understanding of key concepts, while exercises at the end of each chapter provide ample opportunities for practice with the material. Proofs of theorems such as the Uniform Boundedness Theorem, the Open Mapping Theorem, and the Closed Graph Theorem are worked through step-by-step, providing an accessible avenue to understanding these important results. The prerequisites for this book are linear algebra and elementary real analysis, with two introductory chapters providing an overview of material necessary for the subsequent text. Functional Analysis offers an elementary approach ideal for the upper-undergraduate or beginning graduate student. Primarily intended for a one-semester introductory course, this text is also a perfect resource for independent study or as the basis for a reading course.

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Provides an elementary treatment of the subject that establishes the foundation for further study

Enriches understanding of the theory with numerous examples and counterexamples 

Includes many exercises for readers to practice techniques

Dissects proofs of difficult results into small steps to improve understanding

Preface
1. Preliminaries
2. Metric Spaces
3. Special Spaces
4. Normed Spaces
5. Linear Functionals
6. Fundamental Theorems
7. Hilbert Spaces
A. Hilbert Spaces L2(J)
References
Index.
“This textbook is well organized and the proofs are carefully written. … Each chapter is concluded with an interesting note and several exercises, helping the reader to better understand the topics of the chapter. … it will be useful for upper-undergraduate and beginning graduate students.” (Mohammad Sal Moslehian, zbMATH 1398.46001, 2018)
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Sergei Ovchinnikov is Professor Emeritus of Mathematics at San Francisco State University. His other Universitext books are Measure, Integral, Derivative: a Course on Lebesgue's Theory (2013) and Graphs and Cubes (2011). 

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Sergei Ovchinnikov is Professor Emeritus of Mathematics at San Francisco State University. His other Universitext books are Measure, Integral, Derivative: a Course on Lebesgue's Theory (2013) and Graphs and Cubes (2011). 

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