MA 223: Functional Analysis
Credits: 3:0
Prerequisite courses: MA 222, MA 224 and MA 219
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.
Suggested books and references:
- Rudin, Functional Anaysis (2nd Ed.), McGraw-Hill, 2006.
- Yosida, K., Functional Anaysis (4th Edition), Narosa, 1974.
- Goffman, C. and Pedrick, G., First Course in Functional Analysis, Prentice-Hall of India, 1995.