# Herz--Schur multipliers and approximation properties

Presented by:
Andrew McKee Queen&#39;s University Belfast
Date:
Thursday 20th April 2017 - 14:00 to 15:00
Venue:
INI Seminar Room 2
Abstract:
Herz--Schur multipliers of a discrete group have proved useful in the study of $C^*$-algebras, as they can be used to link properties of the group to approximation properties of the reduced group $C^*$-algebra. The development of these ideas has shed light on some $C^*$-algebra properties, and motivated the introduction and study of others.

I will introduce Herz--Schur multipliers, and discuss some of their applications, before describing a generalisation of these functions to multipliers of a $C^*$-dynamical system. In the final part of the talk I will show how the generalised Herz--Schur multipliers can be used to study approximation properties of the reduced crossed product formed by a group acting on a $C^*$-algebra, paralleling the applications of Herz--Schur multipliers; these new tools allow us to study approximation properties of the reduced crossed product without requiring the group to be amenable.

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