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Introduction to Operator Algebras (IntroOpAlg)
Provider: Faculty of Science

Activity no.: 5592-21-07-31 
Enrollment deadline: 08/02/2021
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time08.02.2021, at: 08:00 - 16.04.2021, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserSøren Eilers    E-mail address: eilers@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 3
Scheme groupA (Tues 8-12 + Thurs 8-17)
Exam formContinuous assessment
Exam detailsThere will be given 3 assignments, each of which will count equally towards the final grade.
Exam aidsAll aids allowed
Criteria for exam assessmentThe student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Exam re-examination30 minutes oral examination with 30 min. preparation time during which all aids are allowed. Several internal examiners.
Course workload
Course workload categoryHours
Lectures40.00
Preparation112.00
Exam30.00
Theory exercises24.00

Sum206.00


Content
Commutative Banach algebras, C*-algebras, commutative C*-algebras, continuous function calculus, states and representations, GNS representations, polar decomposition, non-unital C*-algebras and approximate units. AF algebras. Von Neumann algebras. The bicommutant theorem and Kaplansky's density theorem. Borel function calculus.

Learning outcome
Knowledge:
The participants are expected to acquire the knowledge listed above in the course description with an emphasis on function calculus.

Skills:
The participants are expected to be able to understand and apply the Gelfand transform and the GNS-construction, they must understand basic facts about order. They must have some familiarity with important examples of C*-algebras. They must understand the basics of von Neumann algebras.

Competences:
The participants are expected to master the most fundamental concepts and constructions for C*-algebras which are are used in further studies in operator algebras and in non-commutative geometry.

Literature
Kehe Zhu: An introduction to operator algebras (or equivalent), along with handout notes.

Teaching and learning methods
5 hours of lectures plus 3 hours of tutorials per week in 8 weeks (last assignment is due in week 9).

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