Theory of Operator Algebras II
Operator algebras are a central field in modern mathematics, with profound connections to various mathematical disciplines and theoretical physics. In this semester, we will continuously introduce Takesaki's book ``Theory of Operator Algebras I, II, III" following the contents in last semester.
Lecturer
Date
11th March ~ 3rd June, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 13:30 - 15:05 | A7-302 | ZOOM A | 388 528 9728 | BIMSA |
| Friday | 09:50 - 11:25 | A7-302 | ZOOM A | 388 528 9728 | BIMSA |
Prerequisite
Functional Analysis
Syllabus
1. A brief review on Banach Algebras, C*-Algebras and von Neumann Algebras
2. Tensor Products of Operator Algebras and Direct Integrals
3. Types of von Neumann Algebras and Traces
4. Left Hilbert Algebras
5. Weights
6. Modular Automorphism Groups
7. Non-Commutative Integration
8. Crossed Products and Duality
9. Abelian Automorphism Groups
10. Structure of a von Neumann Algebra of Type III
2. Tensor Products of Operator Algebras and Direct Integrals
3. Types of von Neumann Algebras and Traces
4. Left Hilbert Algebras
5. Weights
6. Modular Automorphism Groups
7. Non-Commutative Integration
8. Crossed Products and Duality
9. Abelian Automorphism Groups
10. Structure of a von Neumann Algebra of Type III
Reference
[1] M. Takesaki, Theory of Operator Algebras I, II, III
Audience
Advanced Undergraduate
, Graduate
, Postdoc
Video Public
No
Notes Public
No
Language
Chinese