Cornell Math - MATH 713, Spring 2005

MATH 713: Functional Analysis (Spring 2005)

Instructor: Dmitry Novikov

Meeting Time & Room

Prerequisites: topology and Lebesgue integral.

I will use "Functional analysis" of Rudin and notes of Professor Gross. The topics covered will be roughly as follows:

1. Topological vector spaces. Baire categories, Banach-Steinhause, open (inverse) mapping theorem, Closed
   Graph theorem. Local convexity theorems: Hanh-Banach theorem, Dual spaces and Banach-Alaoglu theorem.
2. Banach algebras. Maximal ideals. C* algebras, Functional calculus.
3. Hilbert space. Spectral theorems. Compact operators. Hilbert-Schmidt theorem. Fredholm theorems. Integral equations.
4. Unbounded operators.
5. Semigroups of operators