# MAT 551: Real Analysis III (Functional Analysis)

# Fall 2013

# Christopher Bishop

Office: 4-112 Mathematics Building

Phone: (631)-632-8274

Dept. Phone: (631)-632-8290

FAX: (631)-632-7631

MWF 11:00am to 11:53am, Math 4-130

Scheduled Final Exam Time 2:15pm-5:00pm, Tuesday, December 17

We will follow the book `Functional Analysis' by Peter Lax, published
by Wiley. There is a wealth of material in the book and ideally you
should know all of it. In practice, however, we shall have to make
some choices about what to cover. Some of the early sections on
linear algebra, Hahn-Banach, Hilbert spaces, uniform boundedness, should
be familiar to you from MAT 544 and 550, so I plan to only review these.
Topics I hope to cover in greater depth include:

--- duality

--- weak convergence and its applications

--- convex sets and extreme points

--- Banach algebras

--- Compact maps and operators

--- Fredholm's theory

--- Spectral theory: Symmetric, Normal, Unitary, Self-Adjoint

--- Groups of Unitary Operators

--- Scattering therory

Grades will be based problem sets, a midterm and final.

### Problem sets (X-Y means Exercise Y of Chapter X.)

Problem Set 1: 1-7, 4-2, 5-3, 5-7, 5-8. Due Friday, Sept 27.

Problem Set 1: 6-7, 6-8, 8-3, 8-6, 10-2, 10-5 Due Friday, Oct 11.

Send the lecturer (C. Bishop) email at:
bishop - at - math.sunysb.edu

Link to
history of mathematics There are a lot
of iteresting articles here. If you know of other math
related sites I should link to, let me know.