MA 503 Functional Analysis (Summer 2018)

Lectures: Mon to Sat 10.30 to 12:30 hrs in Room 113

Office hour: Mon and Thur 3 to 4 pm

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.

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.