OPERATOR THEORY I
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.
Books
- 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