Course

Compact operators on Hilbert Spaces. (a) Fredholm Theory (b) Index, C∗- algebras – noncommutative states and representations, Gelfand-Neumark representation theorem, Von- Neumann algebras; projections, double commutant theorem, L∞ functional calculus, Toeplitzoperators.

1. Arveson, “An invitation to C*-algebras”, Graduate Texts in Mathematics, No. 39.Springer-Verlag, 1976. 
2. N. Dunford and J. T. Schwartz, “Linear operators. Part II: Spectral theory. Self adjointoperators in Hilbert space”, Interscience Publishers John Wiley i& Sons 1963. 
3. R. V. Kadison and J. R. Ringrose, “Fundamentals of the theory of operator algebras. Vol.Elementary theory”, Pure and Applied Mathematics, 100, Academic Press, Inc., 1983.