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Herz--Schur multipliers and approximation properties

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OAS - Operator algebras: subfactors and their applications

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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