Course Archives Theoretical Statistics and Mathematics Unit

Course: Operator Algebras Level: Postgraduate Time: Currently not offered

Syllabus Past Exams Syllabus: i) Definition and examples of Banach and C*algebras, Gelfand theory for abelian Banach and C*algebras, Spectral theorem for bounded normal operators on a Hilbert spaces. ii) General noncommutative C*algebras: basic properties, Positive elements and states, GNS theorem, ideals and quotients of C*algebras, C*algebra of compact operators. iii) Definition of examples of von Neumann algebras, the double commutant theorem and Kaplansky density theorem, abelian von Neumann algebras and the L -functional calculus. iv) Time permitting: discussion on some concrete examples like AF algebras, group C*algebras for discrete countable groups, Cuntz algebras, noncommutative tori etc. Suggested Texts : (a) C*Algebras by Examples, K R Davidson. (b) Functional A Course in Functional Analysis, J B Conway. (c) C*Algebra and Operator Theory, G. J. Murphy. (d) Fundamentals of the theory of operator algebras, volume I and II, R.V. Kadison and J. R. Ringrose. Top of the page Past Exams

Midterm 23.pdf 25.pdf Semestral 23.pdf 25.pdf Supplementary and Back Paper 23.pdf Top of the page

[ Semester Schedule ][ SMU ] [Indian Statistical Institute]