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".
讲师
日期
2025年09月17日 至 12月17日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周三 | 13:30 - 16:55 | A3-4-301 | ZOOM 2 | 638 227 8222 | BIMSA |
修课要求
Functional Analysis
课程大纲
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
参考资料
[1] M. Takesaki, Theory of Operator Algebras I, II, III
听众
Advanced Undergraduate
, Graduate
, 博士后
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笔记公开
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语言
中文