Course

M468 - Operator Theory

Course No: 
M468
Credit: 
4
Prerequisites: 
M401
Approval: 
2014
UG-Elective
Syllabus: 
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, $L_\infty$ functional calculus, Toeplitz operators.
Reference Books: 
  1. W. 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 adjoint operators 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. I. Elementary theory”, Pure and Applied Mathematics, 100, Academic Press, Inc., 1983.
  4. V. S. Sunder, “An invitation to von Neumann algebras”, Universitext, Springer-Verlag, 1987.

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School of Mathematical Sciences

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