# MA 503 Functional Analysis (AS2010)

Lectures: Mon 8:30 to 9:25 pm, Tue 9:30 to 10:25 am, Thu 10.35 to 11:30 am in Room 105
Tutorial: Tue 3.30 pm to 4.55 pm in Room 105

Informations about the course:

Content:
Normed spaces. Continuity of linear maps. Hahn-Banach Extension and Separation Theorems. Banach spaces. Dual spaces and transposes.
Uniform Boundedness Principle and its applications. Closed Graph Theorem, Open Mapping Theorem and their applications. Spectrum of a bounded
operator. Examples of compact operators on normed spaces. Inner product spaces, Hilbert spaces. Orthonormal basis. Projection theorem and
Riesz Representation Theorem.

Text/References:
1. J. B. Conway, Functional Analysis, 2nd Ed., Springer-Verlag, 1990. (also in Springer international edition)
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. (also in Springer international edition)

## Assignments