## Mathematics 421/510 (Functional Analysis)

### Spring 2010

**Instructor: I. Laba (Math Bldg 200, 604-822-4457,
ilaba(at)math.ubc.ca).
**

Lectures: MWF 11-12, WMAX 216.

Office hours: Mon 12-1, Wed 2-3, Fri 1-2, and by appointment.

This course will provide an introduction to functional analysis, with
some applications to other areas of mathematics such as harmonic analysis,
mathematical physics and partial differential equations. The topics will
include the following:
- Banach spaces
- Operator spaces: strong, weak, and weak$^*$ topologies
- Hilbert spaces and their geometry
- Operators on Hilbert spaces: self-adjoint, bounded, compact
- Hahn-Banach theorem, open mapping theorem, closed graph theorem
- Spectral theory for bounded operators
- Fredholm theory for bounded operators

For more details on current and upcoming topics,
click here

**Textbook:** Peter D. Lax, *Functional analysis*, Wiley-Interscience,
New York, 2002, ISBN 0-471-55604-1.

**Prerequisite:** Math 420/507 or equivalent.

**Your course grade** will be based on 6 problem sets, due on January 20, February 3,
March 3, March 17, March 31, and April 21. To allow for minor absences and short illnesses,
the lowest score will be dropped; each of the remaining 5
problem sets will be worth 20% of your grade. There will be no final exam.