Theory of Operator Algebras I
Operator algebras are a central field in modern mathematics, with profound connections to various mathematical disciplines and theoretical physics. In this semester, we will systematically introduce Takesaki's book ``Theory of Operator Algebras I, II, III".
Lecturer
Date
17th September ~ 17th December, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 13:30 - 16:55 | A3-4-301 | ZOOM 2 | 638 227 8222 | BIMSA |
Prerequisite
Functional Analysis
Syllabus
1. Fundamentals of Banach Algebras and C*-Algebras
2. Topologies and Density Theorems in Operator Algebras
3. Conjugate Spaces
4. Tensor Products of Operator Algebras and Direct Integrals
5. Types of von Neumann Algebras and Traces
6. Left Hilbert Algebras
7. Weights
8. Modular Automorphism Groups
9. Non-Commutative Integration
10. Crossed Products and Duality
11. Abelian Automorphism Groups
12. Structure of a von Neumann Algebra of Type III
2. Topologies and Density Theorems in Operator Algebras
3. Conjugate Spaces
4. Tensor Products of Operator Algebras and Direct Integrals
5. Types of von Neumann Algebras and Traces
6. Left Hilbert Algebras
7. Weights
8. Modular Automorphism Groups
9. Non-Commutative Integration
10. Crossed Products and Duality
11. Abelian Automorphism Groups
12. 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