Functional Analysis

4 credits · Graduate

Spectrum of an operator. Analytic functional calculus. Compact operators. Hilbert-Schmidt operators. Spectral theorem for bounded self-adjoint and normal operators. Unbounded self-adjoint operators. Banach algebras. Commutative Gelfand-Naimark theorem. Selected additional topics such as Fredholm operators and Fredholm index, Calkin algebra, Toeplitz operators, semigroups of operators, interpolation spaces, group algebras.