Math 713 — Spring 2002 Functional Analysis

The course will cover basic topics in functional analysis. The main prerequisites are elementary Hilbert space and Banach space principles, as represented in Chapters Four and Five of Rudin's book Real and Complex Analysis. The course will follow a set of notes which will be distributed.

Topics to be covered are:

1. Topological vector spaces
2. Banach algebras
3. The spectral theorem for bounded and unbounded self-adjoint operators
4. Compact operators
5. Semigroups of operators