Pure Math 950 — Fall 2014
Nonself-adjoint Operator Algebras
Meeting Time: Tuesday and Thursday 10:00 -- 11:30
Meeting Place: MC 5046
- Function algebras. These are closed subalgebras of C(X). We will study
their general structure (boundaries, representing measures, Gleason parts)
and answer some questions about analytic structure and approximation.
- Nest algebras. A nest algebra is the set of all bounded operators on a
Hilbert space with a prescribed triangular form. The goal is to develop
their structure, and characterize nest algebras up to isomorphism.
Required Background
- measure theory
- functional analysis
- complex analysis
- Banach algebras
Grading
- Problem Sets 75
- Talk and paper 25
- No exam
Reference Texts
There is no required text for this course.
The following books will be on reserve in the library for 1-day loans.
- Uniform Algebras by T. Gamelin
- Introduction to Function Algebras by A. Browder
- The theory of uniform algebras by E. Stout
- Nest algebras by K. Davidson
Assignments
Talks
Possible topics. Talks will be 50 minutes, and a paper
of about 10 pages with the details is also required.
You are expected to attend all talks.
Here is the schedule.
Tuesday Dec 9 in MC5046
10:00--0:50 Adam Dor-On Close nest algebras are similar (Lance).
11:00--1:50 Richard Mack Cole's example of a proper function algebra where every point is a peak point.
Thursday Dec 11 in MC5158B
10:00--0:50 Boyu Li The Jacobson radical of a nest algebra (Ringrose).
11:00--1:50 Robert Yang McKissick's example of a nontrivial normal function algebra.
Friday Dec 12 in MC5158B
10:00--0:50 Kamyar Moshksar Bishop's generalization of the Stone-Weierstrass theorem.
11:00--1:50 Sam Harris Every derivation on a nest algebra is inner (Christensen).
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