Exercises in Functional Analysis

By: Constantin Costara, D. Popa

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Hardcover | 30 September 2003

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468 Pages

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24.13 x 16.51 x 3.18

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The understanding of results and notions for a student in mathematics requires solving ex- ercises. The exercises are also meant to test the reader's understanding of the text material, and to enhance the skill in doing calculations. This book is written with these three things in mind. It is a collection of more than 450 exercises in Functional Analysis, meant to help a student understand much better the basic facts which are usually presented in an introductory course in Functional Analysis. Another goal of this book is to help the reader to understand the richness of ideas and techniques which Functional Analysis offers, by providing various exercises, from different topics, from simple ones to, perhaps, more difficult ones. We also hope that some of the exercises herein can be of some help to the teacher of Functional Analysis as seminar tools, and to anyone who is interested in seeing some applications of Functional Analysis. To what extent we have managed to achieve these goals is for the reader to decide.

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"The present book is one of the few books available with problems in functional analysis. ... the authors have done a good job in crediting the original sources of the problems. ... The layout and the exposition of the book is very good. The book will be of great help to graduate students in mathematics ... . will also be very helpful to research mathematicians in analysis ... . I strongly recommend the book to any person who is interested in analysis and its applications." (C. D. Aliprantis, Mathematical Reviews, Issue 2005 b)

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms

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Paperback

Published: 18th December 2010

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Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms

Preface	p. vii
Some Standard Notations and Conventions	p. ix
Normed spaces	p. 1
Open, closed, and bounded sets in normed spaces	p. 3
Exercises	p. 4
Solutions	p. 11
Linear and continuous operators on normed spaces	p. 36
Exercises	p. 37
Solutions	p. 42
Linear and continuous functionals. Reflexive spaces	p. 68
Exercises	p. 68
Solutions	p. 72
The distance between sets in Banach spaces	p. 86
Exercises	p. 86
Solutions	p. 92
Compactness in Banach spaces. Compact operators	p. 107
Exercises	p. 108
Solutions	p. 115
The Uniform Boundedness Principle	p. 147
Exercises	p. 147
Solutions	p. 155
The Hahn-Banach theorem	p. 175
Exercises	p. 175
Solutions	p. 180
Applications for the Hahn-Banach theorem	p. 195
Exercises	p. 196
Solutions	p. 199
Baire's category. The open mapping and closed graph theorems	p. 213
Exercises	p. 214
Solutions	p. 220
Hilbert spaces	p. 241
Hilbert spaces, general theory	p. 243
Exercises	p. 245
Solutions	p. 250
The projection in Hilbert spaces	p. 271
Exercises	p. 271
Solutions	p. 281
Linear and continuous operators on Hilbert spaces	p. 305
Exercises	p. 306
Solutions	p. 318
General topological spaces	p. 366
Linear topological and locally convex spaces	p. 368
Exercises	p. 369
Solutions	p. 377
The weak topologies	p. 403
Exercises	p. 405
Solutions	p. 412
Bibliography	p. 444
List of Symbols	p. 447
Index	p. 449
Table of Contents provided by Rittenhouse. All Rights Reserved.

Exercises in Functional Analysis

At a Glance

Hardcover

Industry Reviews

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How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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