## Mathematics 421/510 (Functional Analysis)

### Spring 2012

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

Lectures: Tue Thur 11-12:30, MATH 202

Office hours: Tue 12:30-2, Thur 10-11, 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

A tentative list of current and upcoming topics
is posted here. (I have added more details on the requisite background
in measure and integration theory.) It will be updated as needed. We will mostly follow
the presentation in Lax's textbook, which I find more user-friendly, but
Conway's book is also a good reference.

**Recommended textbooks:**
- John B. Conway,
*A Course in Functional Analysis*,
2nd ed., Springer, 2007.
- Peter D. Lax,
*Functional analysis*, Wiley-Interscience,
New York, 2002.

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

**Your course grade** will be based on 6 problem sets, tentatively due on January 19, February 2,
February 16, March 8, March 22, and April 5. Late assignments will not be accepted except
in the event of illness (with supporting medical documentation), or with prior consent
of the instructor. There will be no final exam.

Homework 1, due on Thursday Jan. 19.

Homework 2, due on Thursday Feb. 2.

Homework 3, due on Thursday Feb. 16.

Homework 4, due on Thursday March 8.

Homework 5, due on Thursday March 22.

Homework 6, due on Thursday April 5.