# Course

## M557 - Operator Algebras

Course No:
M557
Credit:
4
Prerequisites:
M401
Approval:
2014
UG-Elective
Syllabus:
Banach algebras/C*–algebras: Definition and examples; Spectrum of a Banach algebra; Gelfand transform; Gelfand-Naimark theorem for commutative Banach algebras/ C*-algebras; Functional calculus for C*-algebrasPositive cone in a C*-algebra; Existance of an approximate identity in a C*- algebra; Ideals and Quotients of a C*-algebra; Positive linear functionals on a C*-algebra; GNS construction. Locally convex topologies on the algebras of bounded operators on a Hilbert space, von-Neumann’s bi-commutant theorem; Kaplansky’s density theorem. Ruan’s characterization of Operator Spaces (if time permites).
Reference Books:
1. R. V. Kadison, J. R. Ringrose, “Fundamentals of the Theory of Operator Algebras Vol. I”, Graduate Studies in Mathematics 15, American Mathematical Society, 1997.
2. G. K. Pedersen, “C*–algebras and their Automorphism Groups”, London Mathematical Society Monographs 14, Academic Press, 1979.
3. V. S. Sunder, “An Invitation to von Neumann Algebras”, Universitext, Springer-Verlag, 1987.
4. M. Takesaki, “Theory of Operator Algebras Vol. I”, Springer-Verlag, 2002.