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.

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School of Mathematical Sciences

NISERPO- Bhimpur-PadanpurVia- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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