MAT 551: Real Analysis III (Functional Analysis)

Fall 2013

Christopher Bishop

Professor, Mathematics
SUNY Stony Brook

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 -

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.