Course Archives    Theoretical Statistics and Mathematics Unit
Course: Functional Analysis
Level: Postgraduate
Time: Currently not offered
Past Exams

Syllabus: Normed linear spaces, Banach spaces. Bounded linear operators. Dual of a normed linear space. Hahn-Banach theorem, uniform boundedness principle, open mapping theorem, closed graph theorem. Computing the dual of wellknown Banach spaces. Weak and weak* topologies, Banach-Alaoglu Theorem. The double dual.

L^p spaces, Riesz representation theorem for the space C[0,1].

Hilbert spaces, adjoint operators, self-adjoint and normal operators, spectrum, spectral radius, analysis of the spectrum of a compact operator on a Banach space, spectral theorem for bounded self-adjoint operators.

Time permitting: reflexivity; spectral theorem for normal and unitary operators.

Suggested Texts :

1. W. Rudin, Real and complex analysis, McGraw-Hill (1987).

2. W. Rudin, Functional analysis, McGraw-Hill (1991).

3. J. B. Conway, A course in functional analysis, GTM (96), Springer (Indian reprint 2006).

4. K. Yosida, Functional analysis, Springer (Indian reprint 2004).

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Past Exams
06.pdf 09.pdf 10.pdf 12.pdf 14.pdf 16.pdf
06.pdf 09.pdf 10.pdf 12.pdf 14.pdf 16.pdf
04.pdf 09.pdf 10.pdf 12.pdf 16.pdf
10.pdf 12.pdf
Supplementary and Back Paper
04.pdf 10.pdf

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