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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Advanced theory of operator algebras

The course is not on the list Without time-table
Code Completion Credits Range Language
XP01POA ZK 4 2+1 Czech
Lecturer:
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

Some advanced aspects of the theory of operator algebras are treated. In particular, structure of ideals, convex structure of the state space, tensor products, cross products, and modular theory.

Requirements:
Syllabus of lectures:

1. Ideals in operator algebras. Faces in positive cones and duals.

2. Tensor products of Banach spaces and algebras.

3. Tensor products of C* algebras. Projective and injective tensor product. Takeasi theorem on minimal tensor norm.

4. Tensor products of von Neumann algebras. Types of tensor product.

5. Infinite tensor products.

6. Modular theory - mudular operator and modular group.

7. KMS states.

8. Group algebras.

9. Dynamical systems, covariance algebra.

11. Discrete and continuous cross products.

12. Cross products with modular groups. Connes spectrum.

13. Direct integrals of von Neumann algebras.

Syllabus of tutorials:
Study Objective:
Study materials:

1. R.V.Kadison and J.R.Ringrose: Fundamentals of the Theory of Operator Algebras I, II, Academic Press (1986). 2. M.Takesaki: Theory of Operator Algebras I, Berlin, Heidelberg, New York, Springer 2002. 3. J.Hamhalter: Quantum Measure Theory, Kluwer Academic Publishers, Dordrecht 2003.

Note:
Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2020-01-22
For updated information see http://bilakniha.cvut.cz/en/predmet12627504.html