Exercises in Functional Analysis by C. Costara (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book is very interesting. I think that it is a good reference in order to complement a full course of functional analysis because the quantity of exercises is terrific. I recommend the book for everyone!

⭐Good book with many worked out examples. It can be used as companion book while doing course on Functional Analysis.

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