Math 684 (Phillips)
This is the home page for N. C. Phillips'
Math 684 at the University of Oregon,
Fall quarter 2017.
Right now, only administrative information is posted here.
Any additional material will be posted here,
not on Canvas.
(I do not use Canvas.)
This is part of a three quarter sequence.
The second and third quarters will be on C*algebras,
with emphasis on group actions on C*algebras
and their crossed products.
They will be taught by Qingyun Wang.
Course information:

Course number:
Math 684.

Course title: Topics in Functional Analysis.

CRN: 13838.

UO
class schedule page for this course.

Time and place: MWF 12:00 noon12:50 pm, 206 Deady.

Instructor: N. Christopher
Phillips.

Office: 105 Deady.
Please knock.
I can't leave my door open, because if I do I get too many people
asking to borrow my stapler or pencil sharpener, or
where to find the math department office
or nonexistent rooms (such as 350 Deady).

Office hours: M 1:001:50 pm (after this class),
TuW 9:009:50 am (after my other class),
or by
appointment.

Email.
All messages should have a subject starting "Math 684:".
I do not accept binary files or attachments,
except by prior arrangement.
I do not ever accept
Microsoft Word documents, html (web) files, or encoded text messages.
Send 7 bit ASCII plain text only.
That is, use only the characters found on a standard English
language keyboard; no curved quotation marks, curved apostrophes,
accented letters, Greek letters, etc.
(Use TeX codes for mathematical symbols.
Leave extra space in mathematical expressions;
otherwise, they may become unreadable.)

I don't have a specific recommended text;
instead, I will follow different texts for different parts.
Later, I will post here a list of books to look in for parts
of the material.
Course outline (not all of this might actually get done):

A little about bounded operators.

Definition and examples of Banach algebras.

Bott periodicity.

Spectrum, spectral radius.

Weak* topology and Alaoglu's Theorem (with material on general
topological vector spaces left as exercises).

Maximal ideal space of a commutative Banach algebra
and the Gelfand transform.

Proof of the existence of Haar measure on a locally compact group,
probably restricted to the second countable case so as to avoid
measure theoretic technicalities.

Careful identification of the maximal ideal space of L^1 (G) for
a locally compact abelian group G.

Pontryagin duality

Generalized Fourier inversion.

Start the basics of C*algebras (positivity, continuous
functional calculus, states, representations).

Representations of groups from positive functions on them.
Some things that are likely to be omitted from the course for
lack of time (but whose development would make good problem sets):

KreinMilman Theorem.

Irreducible representations.

Fredholm theory.

Holomorphic functional calculus.
Problems:

Set 1:
pdf;
AMSLaTeX.
Warning: Almost no proofreading has been done!

Set 2 (partial):
pdf;
AMSLaTeX.
Warning: No proofreading has been done!
The official final exam time for this course is
10:15 am12:15 pm Monday 4 December 2017.
This page maintained by
N. Christopher Phillips,
email.
Last significant change 22 September 2017.