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Tutorials and extra lectureWritten on 20.04.24 by Michael Hartz Assignments will be released on Tuesdays. The first assignment will come out on April 23, due date May 7. The first tutorial will take place on May 10. There will be no lecture on April 30. Instead, there will be an extra lecture on Friday, April 27, at 12:15 (the tutorial time slot) in HS… Read more Assignments will be released on Tuesdays. The first assignment will come out on April 23, due date May 7. The first tutorial will take place on May 10. There will be no lecture on April 30. Instead, there will be an extra lecture on Friday, April 27, at 12:15 (the tutorial time slot) in HS 4. Relevant dates can also be found in the calendar. |
Operator Algebras
Dates and times
Lecture
Tuesday, 16:00-17:30, HS 4, Building E 2 4
Tutorial
Friday, 12:15-13:45, seminar room 5.
You may submit the solutions for the assignments in teams of up to three people.
Contents
This course is an introduction to the theory of algebras of operators on Hilbert space. Operator algebras lead to insights into the structure of single operators on Hilbert space. Moreover, they are also a fascinating topic in their own right, which has implications to group theory and mathematical physics.
Topics covered:
- Gelfand theory of commutative Banach and C^*-algebras
- States and the GNS construction
- Addenda about locally convex spaces: duality, extreme points and Krein-Milman theorem
- von Neumann algebras
Prerequisites
Functional Analysis
Exam
There will be an oral exam at the end of the semester. In order to be eligible for the exam, you have to achieve at least 50% of the available points on the assignments.
Literature
See here