MM819: An introduction to Operator Algebras
Students taking the course are expected to:
- Have a basic knowledge of topology and functional analysis, corresponding the contents of the courses MM535 and MM543.
- 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.
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. The course builds on the
knowledge acquired in the courses MM535 (Topology) and MM543 (Measure
and integration and Banach spaces) and gives the student the necessary
prerequisites to specialize in operator algebra theory during their
In relation to the competence profile of the degree it is the explicit focus of the course to:
- Give the competence to take responsibility for the academic development and specialization.
- Give the competence to develop an overview of the interplay between different mathematical disciplines.
- Give skills to work concretely with Hilbert spaces and their operators.
- Give skills to use central functional analytic tools (the Hahn Banach theorem and its consequences)
- Give knowledge and understanding of concrete examples of operator algebras.
- Give knowledge of the theory of commutative C*-algebras.
- Give knowledge of the theory of operators on Hilbert spaces.
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.
The following main topics are contained in the course:
- The Gelfand transform
- Representation theory for C*-algebras
- The Gelfand Naimark theorem
- Compact operators and the spectral theorem.
Exam element a)
To be announced during the course
Indicative number of lessons
sessions will be devoted to learn material in depth. Interactive
teaching will be used.
- The students are expected to familiarize themselves with the material covered in the lectures.
- To acquire knowledge of selected topics independently.
|08 - 09|
|09 - 10|
|10 - 11|
|11 - 12|
|12 - 13|
|13 - 14|
|14 - 15|
|15 - 16|