# Course Identification

## Lecturers and Teaching Assistants

## Course Schedule and Location

## Field of Study, Course Type and Credit Points

## Comments

## Prerequisites

Basic courses in functional analysis and measure theory

## Restrictions

## Language of Instruction

## Attendance and participation

## Grade Type

## Grade Breakdown (in %)

## Evaluation Type

**Other**

## Scheduled date 1

## Estimated Weekly Independent Workload (in hours)

## Syllabus

**What is this course all about?**

An operator algebra on a Hilbert space *H* is a closed subalgebra of the algebra *B(H)* of bounded operators on *H*. These include all closed algebras of continuous functions on a compact space, matrix algebras, and many more. My intention is to divide the course into two halves: the first will focus on operator algebras, with the first few weeks dedicated to self-adjoint ones, namely C*-algebras, and the second will be devoted to the fruitful interaction between operator algebras and groups

The very flexible plan is:

- C*-algebras (3–5 lectures)
- Operator algebras and operator systems (3–4 lectures)
- Groups, dynamics, and related operator algebras (5–7 lectures)

## Learning Outcomes

Upon successful completion of this course students should be able to

demonstrate an understanding of the concepts of operator algebras as well as their relations to dynamics.

## Reading List

- D. P. Blecher and C. L. Merdy.
*Operator Algebras and Their Modules — An Operator Space Approach*. The Clarendon Press, Oxford University Press, Oxford, 2004. - E. Breuillard, M. Kalantar, M. Kennedy, and N. Ozawa. C*-simplicity and the unique trace property for discrete groups.
*Publ. Math. Inst. Hautes Études Sci.*, 126:35–71, 2017. - N. P. Brown and N. Ozawa.
*C*-algebras and Finite-Dimensional Approximations.*American Mathematical Society, Providence, 2008. - K. R. Davidson.
*C*-algebras by example*, volume 6 of Fields Institute Monographs. American Mathematical Society, Providence, RI, 1996. - M. Kalantar and M. Kennedy. Boundaries of reduced C ∗ -algebras of discrete groups.
*J. Reine Angew. Math.*, 727:247–267, 2017. - V. Paulsen.
*Completely Bounded Maps and Operator Algebras*, volume 78 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2002.