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 heorem, closed graph theorem. The Banach- Steinhaus theorem. Hilbert spaces, Riesz representation theorem, orthogonal complements, bounded operators on a Hilbert space. The spectral theorem for compact, self-adjoint operators. Recommended Books