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Functional Analysis: Banach spaces, Hahn-Banach theorem, Open mapping & Closed graph theorems, Principle of Uniform Boundedness, Boundedness & continuity of Linear transformations, Dual spaces, Embedding in the second dual, Hilbert spaces, orthonomal sets, Bessel’s inequality, Parseval’s identity, Riesz Representation theorem, Self-adjoint, Unitary & Normal linear operators on Hilbert spaces.