Functional Analysis course

Budapest Semesters in Mathematics

Spring 2012

Monday 12-14, Wednesday 10-12 (Room 104)

Course description


Exercise sheets

0. Homework set, Week 1 Solutions
1. Infinite dimensional vector spaces Solutions
2. Metric spaces and convergence Solutions
3. Norms and bounded operators Solutions
4. Bounded linear functionals and dual spaces Solutions
5. Extension of functionals; Hahn-Banach theorem Solutions
6. Baire category theorem and its consequences Solutions
7. Spectra of operators Solutions
8. Compact operators Solutions
9. Lp spaces Solutions
10. Inner product spaces Solutions
11. Hilbert spaces Solutions
12. Orthonormal bases Solutions
13. Operators on Hilbert spaces Solutions
14. Normal operators Solutions
15. Special operators Solutions
16. Spectrum; polar decomposition Solutions
Extra problems


Exams

Midterm exam Solutions
Final exam Solutions