Functional analysis : an introductory course /

Functional analysis : an introductory course /

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Bibliographic Details
Author / Creator:	Ovchinnikov, Sergeĭ, author.
Imprint:	Cham : Springer, 2018.
Description:	1 online resource (XII, 205 pages) : illustrations
Language:	English
Series:	Universitext, 0172-5939 Universitext,
Subject:	Mathematics. Functional analysis. Functional analysis. Mathematics.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11664215

Hidden Bibliographic Details
ISBN:	3319915126 3319915118 9783319915111 9783319915128
Digital file characteristics:	text file PDF
Notes:	Includes bibliographical references and index.
Summary:	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 Bounded Theory, 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.
Other form:	Print version: 9783319915111
Standard no.:	10.1007/978-3-319-91512-8 9783319915111

Table of Contents:

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.