Mth 617 Functional Analysis I

Hilbert and Banach spaces, the Hahn-Banach, open mapping, and closed graph theorems. Compact, self-adjoint, normal, and Fredholm operators. Locally convex spaces, weak topologies, duality. Banach- and C* -algebras, spectral theory. This is the first course in a sequence of three: Mth 617, Mth 618, and Mth 619 which must be taken in sequence. Expected preparation: Mth 412/Mth 512.