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

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