Exercises in Functional Analysis

• 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.

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)