# MA8107 Operator Algebras

## Contents of the course

We will cover a variety of topics in the theory of operator algebras, in particular of C*-algebras and von Neumann algebras.

The goal is to expose students to the basic notions in the theory of operator algebras and to prepare them to understand fundamentals used in current areas of active research.

In order to gain a deeper understanding of the abstract concepts we examine a number of examples that illustrate different aspects of the theory, such as group algebras, convolution algebras and noncommutative tori. Concretely, we are going to discuss the unexpected apperance of operator algebras in applied harmonic analysis and basic notions of noncommutative geometry.

## Lectures

Mandag 10:15-12:00
Sted: R40 (Realfagsbygget)
Tirsdag 10:15-12:00
Sted: KJL22
(Første gang tirsdag 21.08)

## Prerequisites

Functional analysis TMA4230 is the official prerequisite, but Linear Methods should suffice for an understanding of a large part of the material.

## Textbooks

• “C*-algebras and operator theory” by Gerard J. Murphy. Boston : Academic Press, 1990.
• ”C*-algebras by example” av Kenneth R. Davidson. Fields Institute monographs; vol. 6 Providence, R.I. : American Mathematical Society, 1996.
• I.F.Putnam. "Lecture notes on C*-algebras".
• Pierre de la Harpe, Vaughan Jones. "An introduction to C*-algebras". (Lecture notes.)
• E. C. Lance. Hilbert C*-modules — a toolkit for operator algebraists. London Math. Soc. Lecture Note Series 210. Cambridge Univ. Press, Cambridge, 1995.
• "Morita equivalence and continuous-trace C*-algebras" by Iain Raeburn, Dana P. Williams. Mathematical surveys and monographs ; no. 60. Providence, R.I. : American Mathematical Society, 1998.
• "An Introduction to Noncommutative Geometry" by Joseph C. Várilly. EMS series of lectures in mathematics European Mathematical Society, 2006.
• "Crossed products of C*-algebras" by Dana P. Williams. Mathematical surveys and monographs vol. 134 (2007)