Exercises in functional analysis
- Popa, Dumitru.
- Includes bibliographical references (p. -446) and index.
- 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.
- (source: Nielsen Book Data)
- Publisher's Summary
- This book contains almost 450 exercises, all with complete solutions; it provides supplementary examples, counter-examples, and applications for the basic notions usually presented in an introductory course in Functional Analysis. Three comprehensive sections cover the broad topic of functional analysis. A large number of exercises on the weak topologies is included.
(source: Nielsen Book Data)
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Table of contents
Table of Contents Exercises in functional analysis
- Publication date
- by Constantin Costara and Dumitru Popa.
- Kluwer texts in the mathematical sciences ; v. 26