# MA 824 Functional Analysis (SS2010)

Tue and Fri 3:30 pm to 4.55 pm in Room 105

Informations about the course:

Content:
Review of normed linear spaces, Hahn-Banach theorems, t.v.s., duals, uniform boundedness principle, open mapping theorem, closed graph theorem,
Riesz Lemma, weak topologies, weak and weak* convergence, reflexivity in the setting of normed linear spaces, Compact operators,
integral operators, spectral theorem for compact self adjoint operators, 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, Birkhäuser, 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