Exercises in functional analysis

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Title:

Personal Author:

Costara, C.

Series:

Kluwer texts in the mathematical sciences ; 26

Publication Information:

The Nethelands : Kluwer Academic Publishers, 2003

Physical Description:

x, 451 p. ; 25 cm.

ISBN:

9781402015601

Subject Term:

Functional analysis -- Problems, exercises, etc.

Added Author:

Popa, Dumitru

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010225867	QA320 C67 2003	Open Access Book	Book	Searching... Unknown
Searching... PSZ KL	30000010226097	QA320 C67 2003	Open Access Book	Book	Searching... Unknown

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.

Preface	p. vii
Some Standard Notations and Conventions	p. ix
Part I Normed spaces	p. 1
Chapter 1. Open, closed, and bounded sets in normed spaces	p. 3
1.1 Exercises	p. 4
1.2 Solutions	p. 11
Chapter 2. Linear and continuous operators on normed spaces	p. 36
2.1 Exercises	p. 37
2.2 Solutions	p. 42
Chapter 3. Linear and continuous functionals. Reflexive spaces	p. 68
3.1 Exercises	p. 68
3.2 Solutions	p. 72
Chapter 4. The distance between sets in Banach spaces	p. 86
4.1 Exercises	p. 86
4.2 Solutions	p. 92
Chapter 5. Compactness in Banach spaces. Compact operators	p. 107
5.1 Exercises	p. 108
5.2 Solutions	p. 115
Chapter 6. The Uniform Boundedness Principle	p. 147
6.1 Exercises	p. 147
6.2 Solutions	p. 155
Chapter 7. The Hahn-Banach theorem	p. 175
7.1 Exercises	p. 175
7.2 Solutions	p. 180
Chapter 8. Applications for the Hahn-Banach theorem	p. 195
8.1 Exercises	p. 196
8.2 Solutions	p. 199
Chapter 9. Baire's category. The open mapping and closed graph theorems	p. 213
9.1 Exercises	p. 214
9.2 Solutions	p. 220
Part II Hilbert spaces	p. 241
Chapter 10. Hilbert spaces, general theory	p. 243
10.1 Exercises	p. 245
10.2 Solutions	p. 250
Chapter 11. The projection in Hilbert spaces	p. 271
11.1 Exercises	p. 271
11.2 Solutions	p. 281
Chapter 12. Linear and continuous operators on Hilbert spaces	p. 305
12.1 Exercises	p. 306
12.2 Solutions	p. 318
Part III General topological spaces	p. 366
Chapter 13. Linear topological and locally convex spaces	p. 368
13.1 Exercises	p. 369
13.2 Solutions	p. 377
Chapter 14. The weak topologies	p. 403
14.1 Exercises	p. 405
14.2 Solutions	p. 412
Bibliography	p. 444
List of Symbols	p. 447
Index	p. 449

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