Exercises in functional analysis/
Constantin Costara and Dumitru Popa
- New York: Springer, 2003.
- x, 451 p. ; 25 cm.
- (Kluwer texts in the mathematical sciences), v. 26 .
Part I. Normed spaces -- Chapter 1. Open, closed, and bounded sets in normed spaces -- 1.1. Exercises -- 1.2. Solutions -- Chapter 2. Linear and continuous operators on normed spaces -- 2.1. Exercises -- 2.2. Solutions -- Chapter 3. Linear and continuous functionals. Reflexive spaces -- 3.1. Exercises -- 3.2. Solutions -- Chapter 4. The distance between sets in Banach spaces -- 4.1. Exercises -- 4.2. Solutions -- Chapter 5. Compactness in Banach spaces. Compact operators -- 5.1. Exercises -- 5.2. Solutions -- Chapter 6. The Uniform Boundedness Principle -- 6.1. Exercises -- 6.2. Solutions -- Chapter 7. The Hahn-Banach theorem -- 7.1. Exercises -- 7.2. Solutions -- Chapter 8. Applications for the Hahn-Banach theorem -- 8.1. Exercises -- 8.2. Solutions -- Chapter 9. Baire's category. The open mapping and closed graph theorems -- 9.1. Exercises -- 9.2. Solutions -- Part II. Hilbert spaces -- Chapter 10. Hilbert spaces, general theory -- 10.1. Exercises -- 10.2. Solutions -- Chapter 11. The projection in Hilbert spaces -- 11.1. Exercises -- 11.2. Solutions -- Chapter 12. Linear and continuous operators on Hilbert spaces -- 12.1. Exercises -- 12.2. Solutions -- Part III. General topological spaces -- Chapter 13. Linear topological and locally convex spaces -- 13.1. Exercises -- 13.2. Solutions -- Chapter 14. The weak topologies -- 14.1. Exercises -- 14.2. Solutions.