Exercises in Functional Analysis (Texts in the Mathematical Sciences 26 2003 ed.)

Exercises in Functional Analysis (Texts in the Mathematical Sciences 26 2003 ed.)

By: Constantin Costara (author), Dumitru Popa (author)Hardback

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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.


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.

Product Details

  • ISBN13: 9781402015601
  • Format: Hardback
  • Number Of Pages: 454
  • ID: 9781402015601
  • weight: 1830
  • ISBN10: 1402015607
  • edition: 2003 ed.

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