Pure Math 810 - Operator theory, Banach and C*-Algebras - Winter 2014

Meeting Time: Tuesday and Thursday 10:30--11:50 
Room: 	      MC 5403 


Required Background
A course in functional analysis.
Courses in complex analysis and measure theory are very useful.


Course Outline
1. Banach algebras: spectrum, functional calculus
2. Commutative Banach algebras
3. Non-commutative Banach algebras
4. C*-algebras: ideals, states, GNS construction
5. Von Neumann algebras: the density theorems 
6. Spectral theorem for normal operators. 


Reference Books

• An Introduction to Operator Algebras by Laurent Marcoux, posted online at 
  http://www.math.uwaterloo.ca/~lwmarcou/ under Teaching/Notes for PMath 810.

• Complete normed algebras by F.F. Bonsall and J. Duncan, Springer, 1973.

• C*-Algebras by Example by K.R. Davidson, AMS, 1996.



Grading
Assignments       	70 %
Seminar and paper	30 %
No exams

Assignments

Assignment 1 ( the LaTeX code ) due January 31.

Assignment 2 ( the LaTeX code ) due February 14.

Assignment 3 ( the LaTeX code ) due March 14.

Assignment 4 ( the LaTeX code )

Comments and Solutions

Comments on Assignment 1

Comments on Assignment 2

Talks

Possible topics. Talks will be 25 minutes, and a paper of about 10 pages with the details is also required. 

Talk Schedule (rooms TBA)

Monday April 8
	10:30	Adam Humeniuk
	11:00	Ben Anderson-Sackaney
	11:30	Dan Ursu

Tuesday April 9
	10:30	Finlay Rankin
	11:00	Tianyi Zhou
	11300	Wanchun Shen
	12:00	Erlang Surya

Thursday April 11
	10:30	Adina Goldberg
	11:00	Padraig Daly
	11:30	Chris Hawthorne

Friday April 12
	10:30	Greg Patchell
	11:00	Jeff Samuelson
	11:30	Zhenyuan Zhang