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MM819: An introduction to Operator Algebras (5 ECTS)

STADS: 13005101

Master's level course

Teaching period
The course is offered in the autumn semester.

Teacher responsible

Additional teachers

Group Type Day Time Classroom Weeks Comment
Common I Tuesday 12-14 IMADA Seminarrum 06-13
Common I Wednesday 16-18 Spørg underviseren 06-13
Common I Friday 10-12 Spørg underviseren 06-13
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Ubegrænset deltagerantal. 3.kvartal.


Academic preconditions:
The content of MM517 Measure and Integration Theory and MM514 Hilbert and Banach Spaces is assumed to be known.

Course introduction
The purpose of this course is to present the basic theory of algebras of operators on Hilbert spaces with emphasis on C*-algebra theory.

Expected learning outcome
At the end of the course the student will be able to:

  • reproduce definitions and results, together with their proofs, within the scope of the syllabus of the course
  • apply these results to examples
  • formulate and present definitions, proofs and computations in a mathematically rigorous way
Subject overview
The Gelfand representation of and Abelian Banach algebra, representation theory of non-commutative C*-algebras, Gelfand-Naimarks theorem, the Kaplansky density theorem, the second dual A** of a C*-algebra and applications.

  • Meddeles ved kursets start.: .

This course uses e-learn (blackboard).

Prerequisites for participating in the exam

Assessment and marking:
Mandatory assignments , grades according to the Danish 7-point scale, internal examiner.

The re-exam may be different than the ordinary exam.

Reexamination according to the rules approved by the study board.

Expected working hours
The teaching method is based on three phase model.

Forelæsninger: 28 timer
Eksaminatorietimer/opgaveregning: 14 timer
Educational activities

This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.