# MA 824 Functional Analysis (Spring 2012)

Mon and Thur 3:30 pm to 4.55 pm in Room 105

Informations about the course:

Content:
Review of normed linear spaces, Hahn-Banach theorems,
duals, uniform boundedness principle, open mapping theorem, closed
graph theorem, Riesz representation
theorem on Hilbert spaces, weak topologies, weak and weak* convergence,
reflexivity in the setting of normed linear spaces, Compact operators,
Sturm-Liouville problems, spectral theorem for compact self adjoint
operators, spectral projections, spectral decomposition theorem, spectral theorem
for a bounded normal operator.

Text/References:
1. J. B. Conway, Functional Analysis, 2nd Ed., Springer-Verlag, 1990.
2. I. Gohberg and S. Goldberg, Basic Operator Theory, BirkhĂ¤user, 1980.
3. B. V. Limaye, Functional Analysis, 2nd Ed., New Age International Publishers, 1996.
4. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis, 2nd Ed., Academic Press, 1980.
5. W. Rudin, Functional Analysis, Tata McGraw Hill, 1974.
6. V. S. Sunder, Functional analysis- Spectral theory, TRIM, Hindustan Book Agency, 1997.
7. K. Yosida, Functional Analysis, 5th Ed., Narosa, 1979.

## Assignments