MA 323: Operator Theory
Credits: 3:0
Review of basic notions from Banach and Hilbert space theory.
Bounded linear operators: Spectral theory of compact, self adjoint, and normal operators. Sturm-Liouville problems, Green’s function, Fredholm integral operators.
Unbound linear operators on Hilbert spaces: Symmetric and self adjoint operators, Spectral theory, Banach algebras, Gelfand representation theorem, $C^*$-algebras, Gelfand-Naimark-Segal construction.
Suggested books and references:
- Conway, J. B., A course in Functional Analysis, Springer-Verlag, 1990.
- Rudin, W., Functional Analysis, Tata Mcgraw-Hill, 1974.
- Berberian, S. K., Lectures in Functional Analysis, Frederic Ungar, 1955.