Normed linear spaces, Banach spaces, Hilbert spaces, Banach Algebras, Hahn-Banach extension theorems, Banach-Steinhaus theorem, bounded linear operators, convex sets, linear functionals, duality, reflexive spaces, weak topology and weak convergence, Banach fixed point theorem, uniform boundedness principle, open mapping theorem, closed graph theorem, representation of functionals on Hilbert spaces (Riesz Representation Theorem. (3 credit hours).
