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Applied Functional Analysis (MATH302)

Vector Spaces. Normed spaces. Banach spaces. Properties of normed spaces. Continuity and convergence in Normed spaces. Topology in Normed spaces. Bounded and continuous linear operators. Linear functionals. Normed Spaces of operators. Dual space. Inner product space. Hilbert Space. Properties of inner product spaces. Orthogonal complements and direct sums. Open mapping theorem. Closed linear operators. Closed graph theorem.

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