## Description

Banach Spaces with examples of ([a, *b*]) and C([*a*, *b*]), Hahn Banach theorem, open mapping theorem, closed graph theorem, Baire Category theorem, Banach Steinhauns theorem (uniform boundedness principle), Boundedness and continuity of linear transformation, Dual Spaces, embedding in second dual.

** **Hilbert space, orthonormal basis, Bessel’s inequality, Riesz Fischer theorem, Parseval’s identity, bounded Linear functionals; projections, Riesz Representation theorem, adjoint operators, self adjoint, normal, unitary and isometric operators.

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