Course Archives    Theoretical Statistics and Mathematics Unit
Course: Functional Analysis
Level: Postgraduate
Time: Currently not offered
Syllabus
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
Midterm
06.pdf 09.pdf 10.pdf 12.pdf 14.pdf 16.pdf
Solution
06.pdf 09.pdf 10.pdf 12.pdf 14.pdf 16.pdf
Semestral
04.pdf 09.pdf 10.pdf 12.pdf 16.pdf
Solution
10.pdf 12.pdf
Supplementary and Back Paper
04.pdf 10.pdf

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