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, Banach-Steinhaus theorem, Hilbert spaces, Reisz representation theorem, Orthonormal sets, Orthogonal complements, Elements of operator theory.
Books
- Simmons, G.F., Introduction to Topology and modern Analysis, McGraw-Hill International Edition, 1963.
- Taylor, A.E., Introduction to Functional Analysis, Wiley International Edition, 1958.
- Bachman, G. and Narici, L., Functional Analysis, Academic Press, 1966.