# Exercises in Functional Analysis

Springer Science & Business Media, Sep 30, 2003 - Mathematics - 451 pages
1 Review
Reviews aren't verified, but Google checks for and removes fake content when it's identified
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

Reviews aren't verified, but Google checks for and removes fake content when it's identified
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