Exercises in Functional Analysis

Front Cover
Springer Science & Business Media, Sep 30, 2003 - Mathematics - 451 pages
1 Review
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.
 

What people are saying - Write a review

User Review - Flag as inappropriate

functional

Contents

Open closed and bounded sets in normed spaces
3
11 Exercises
4
12 Solutions
11
Linear and continuous operators on normed spaces
36
21 Exercises
37
22 Solutions
42
Linear and continuous functional Reflexive spaces
68
32 Solutions
72
Baires category The open mapping and closed graph theorems
213
92 Solutions
220
Part II Hilbert spaces
241
Hilbert spaces general theory
243
101 Exercises
245
102 Solutions
250
The projection in Hilbert spaces
271
Linear and continuous operators on Hilbert spaces
305

The distance between sets in Banach spaces
86
42 Solutions
92
Compactness in Banach spaces Compact operators
107
51 Exercises
108
52 Solutions
115
The Uniform Boundedness Principle
147
62 Solutions
155
The HahnBanach theorem
175
72 Solutions
180
Applications for the HahnBanach theorem
195
82 Solutions
199
121 Exercises
306
122 Solutions
318
Part III General topological spaces
366
Linear topological and locally convex spaces
368
132 Solutions
377
The weak topologies
403
142 Solutions
412
Bibliography
444
List of Symbols
447
Index
449
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information