Overview

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.

Full Product Details

Author:   C. Costara ,  D. Popa
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of hardcover 1st ed. 2003
Volume:   26
Dimensions:   Width: 16.00cm , Height: 2.30cm , Length: 24.00cm
Weight:   0.706kg
ISBN:  

9789048163991

ISBN 10:   9048163994
Pages:   454
Publication Date:   18 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

I: Normed spaces.- 1. Open, closed, and bounded sets in normed spaces.- 2. Linear and continuous operators on normed spaces.- 3. Linear and continuous functionals. Reflexive spaces.- 4. The distance between sets in Banach spaces.- 5. Compactness in Banach spaces. Compact operators.- 6. The Uniform Boundedness Principle.- 7. The Hahn—Banach theorem.- 8. Applications for the Hahn—Banach theorem.- 9. Baire’s category. The open mapping and closed graph theorems.- II: Hilbert spaces.- 10. Hilbert spaces, general theory.- 11. The projection in Hilbert spaces.- 12. Linear and continuous operators on Hilbert spaces.- III: General topological spaces.- 13. Linear topological and locally convex spaces.- 14. The weak topologies.- List of Symbols.

Reviews

From the reviews: 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)

From the reviews: 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)

From the reviews: 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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