Costara C., Popa D. Exercises in Functional Analysis

Springer, 2003. - 451 pages.The understanding of results and notions for a student in mathematics requires solving exercises. 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.We have also tried to show the reader, on the one hand, the various and sometimes unexpected connections between the usual parts of a course in Functional Analysis and other topics in mathematics, and, on the other hand, the fine interplay between the topics in the field of Functional Analysis. As a consequence we have decided to include in our chapters some exercises which are connected with the respective chapter, even if the solution we give requires the use of notions and results which are usually studied later in a course in Functional Analysis. We hope that this option will be to the benefit of the reader. When we refer to an exercise from the same chapter we only indicate the number for that exercise, and when we refer to an exercise from another chapter we also indicate the chapter's number.