MM819: An introduction to Operator Algebras

The Study Board for Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310002102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Master's level course approved as PhD course

STADS ID (UVA): N310002101
ECTS value: 5

Date of Approval: 12-03-2025


Duration: 1 semester

Version: Approved - active

Entry requirements

MM549 og MM845 or similar courses.

Academic preconditions

Students taking the course are expected to:

  • Have a basic knowledge of topology and functional analysis, corresponding the contents of the courses MM549 and MM845.
  • Be able to use basic arguments from topology.
  • Be able to work independently with linear algebra.
  • Have a basic knowledge of the theory of groups and rings.

Course introduction

The aim of the course is to introduce the student to the basics of the
theory of operator algebras, with emphasis on the theory of C*-algebras
and operators on Hilbert spaces. The material covered is important in
almost all aspects of modern analysis. 

Expected learning outcome

The learning objectives of the course are that the student demonstrates the ability to:

  • Reproduce definitions and results, including their proofs, covered in the course.
  • Be able to use these results to analyse concrete examples.
  • Formulate and present definitions, proofs and calculations in a mathematically rigorous way.

Content

The following main topics are contained in the course:

  • The Gelfand transform
  • Representation theory for C*-algebras
  • The Gelfand Naimark theorem
  • The spectral theorem for selfadjoint operators

Literature

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

Autumn

Tests

Mandatory assignments

EKA

N310002102

Assessment

Second examiner: Internal

Grading

7-point grading scale

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value

5

Additional information

The re-exam is changed to an oral exam if there are 4 or fewer students enrolled. At the oral re-exam, the students draw a random assignment among the mandatory assignments (which make up the ordinary exam) and must now present the assignment at the blackboard.

Indicative number of lessons

42 hours per semester

Teaching Method

Planned lessons:
Total number of planned lessons: 42
Hereof:
Common lessons in classroom/auditorium: 42


Lectures will introduce general concepts and theory and exercise sessions will be devoted to learn material in depth. Active learning will be used.

Other planned teaching activities:
  • The students are expected to familiarize themselves with the material covered in the lectures.
  • To acquire knowledge of selected topics independently

Teacher responsible

Name E-mail Department
David Kyed dkyed@imada.sdu.dk Analyse

Additional teachers

Name E-mail Department City
Wojciech Szymanski szymanski@imada.sdu.dk Analyse

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.