MA 824 Functional Analysis (Spring 2018)

Wed and Fri 11:05 to 12.30 pm in Room 114

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, compact operators, spectrum of a bounded operator,

spectral theorem for a bounded self-adjoint, operator, unbounded operators, spectral theorem for an unbounded normal operator.

Text/References:

1. J. B. Conway, Functional Analysis, 2nd Ed., Springer-Verlag, 1990.

2. I. Gohberg and S. Goldberg, Basic Operator Theory, Birkhauser, 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.