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).