**
FUNCTIONAL ANALYSIS**

Basic topological concepts, Metric spaces, Normed linear spaces, Banach spaces, Bounded linear functionals and dual spaces, Hahn-Banach theorem. Bounded linear operators, open-mapping theorem, closed graph theorem. The Banach-Steinhaus theorem. Hilbert spaces, Riesz representation theorem, orthogonal complements, bounded operators on a Hilbert space up to (and including) the spectral theorem for compact, self-adjoint operators.

**Recommended Books**

- Goffman, C. and Pedrick, G., First Course in Functional Analysis, Prentice-Hall of India, 1995.
- Rudin, W., Functional Anaysis, 2nd Edition, Tata McGraw-Hill, 2006
- Yosida, K., Functional Anaysis, 4th Edition, Narosa,1974