Course Archives Theoretical Statistics and Mathematics Unit
Course: Operator Theory
Level: Postgraduate
Time: Currently not offered
Syllabus
Past Exams


Syllabus :
1. Compact operators on Hilbert Spaces: Fredholm Theory, Index.
2. C*- algebras - noncommutative states and representations, Gelfand-Neumark representation theorem.
3. Von-Neumann Algebras; Projections, Double Commutant theorem, L functional Calculus.
4. Toeplitz operators.

Suggested Texts :
1. W. Arveson, An invitation to C*-algebras, GTM (39), Springer-Verlag (1976).
2. N. Dunford and J. T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, Interscience Publishers John Wiley (1963).
3. R. V. Kadison and J. R. Ringrose, Fundamentals of the theory of operator algebras. Vol.I. Elementary theory, Pure and Applied Mathematics (100), Academic Press (1983).
4. V. S. Sunder, An invitation to von Neumann algebras, Universitext, Springer- Verlag (1987).

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Past Exams
Midterm
11.pdf 17.pdf
Semestral
05.pdf 07.pdf 11.pdf 11a.pdf 17.pdf
Supplementary and Back Paper
07.pdf 17.pdf

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