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.