Herz--Schur multipliers and approximation properties

50 mins 55 secs, 631.53 MB, WebM 640x360, 29.97 fps, 44100 Hz, 1.65 Mbits/sec

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Description:	McKee, A (Queen's University Belfast) Thursday 20th April 2017 - 14:00 to 15:00


Created:	2017-04-28 10:58
Collection:	Operator algebras: subfactors and their applications
Publisher:	Isaac Newton Institute
Copyright:	McKee, A
Language:	eng (English)


Abstract:	Herz--Schur multipliers of a discrete group have proved useful in the study of C∗C∗-algebras, as they can be used to link properties of the group to approximation properties of the reduced group C∗C∗-algebra. The development of these ideas has shed light on some C∗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∗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∗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.

Abstract:

Herz--Schur multipliers of a discrete group have proved useful in the study of C∗C∗-algebras, as they can be used to link properties of the group to approximation properties of the reduced group C∗C∗-algebra. The development of these ideas has shed light on some C∗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∗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∗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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