The University of Southampton
University of Southampton Institutional Repository

On approximation properties of group C* - algebras

On approximation properties of group C* - algebras
On approximation properties of group C* - algebras
In this thesis we study analytic techniques from operator theory that encapsulate geometric properties of a group. Rapid Decay Property (Property RD) provides estimates for the operator norm of elements of the group ring (in the left-regular representation) in terms of the Sobolev norm. Roughly, property RD is the noncommutative analogue of the fact that smooth functions are continuous. Our work then concentrates on a particular form of an approximation property for the reduced C*- algebra of a group: the invariant approximation property. This statement captures a particular relationship between three important operator algebras associated with a group: the reduced C*- algebra, the von Neumann algebra, and the uniform Roe algebra. The main result is the proof of the invariant approximation property for groups equipped with a conditionally negative length function. We prove also that the invariant approximation property passes to sub- groups and then discuss the behaviour of the invariant approximation property with the respect to certain classes of extensions. We show that the invariant approximation property passes to direct products with finite group. We show that the invariant approximation property passes to extensions of the following form. If G is a discrete group and H is a finite index normal subgroup of G with IAP, then G has IAP
Kankeyanathan, Kannan
60eb031b-18d4-4e25-92e0-fa488b0fe784
Kankeyanathan, Kannan
60eb031b-18d4-4e25-92e0-fa488b0fe784
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543

Kankeyanathan, Kannan (2011) On approximation properties of group C* - algebras. University of Southampton, School of Mathematics, Doctoral Thesis, 116pp.

Record type: Thesis (Doctoral)

Abstract

In this thesis we study analytic techniques from operator theory that encapsulate geometric properties of a group. Rapid Decay Property (Property RD) provides estimates for the operator norm of elements of the group ring (in the left-regular representation) in terms of the Sobolev norm. Roughly, property RD is the noncommutative analogue of the fact that smooth functions are continuous. Our work then concentrates on a particular form of an approximation property for the reduced C*- algebra of a group: the invariant approximation property. This statement captures a particular relationship between three important operator algebras associated with a group: the reduced C*- algebra, the von Neumann algebra, and the uniform Roe algebra. The main result is the proof of the invariant approximation property for groups equipped with a conditionally negative length function. We prove also that the invariant approximation property passes to sub- groups and then discuss the behaviour of the invariant approximation property with the respect to certain classes of extensions. We show that the invariant approximation property passes to direct products with finite group. We show that the invariant approximation property passes to extensions of the following form. If G is a discrete group and H is a finite index normal subgroup of G with IAP, then G has IAP

PDF
Kannan_Kankayanathan_PhD_Thesis.pdf - Other
Download (691kB)

More information

Published date: 11 October 2011
Organisations: University of Southampton, Mathematical Sciences

Identifiers

Local EPrints ID: 208331
URI: https://eprints.soton.ac.uk/id/eprint/208331
PURE UUID: a79ba653-736e-4679-9a57-95e87fe00e41

Catalogue record

Date deposited: 20 Jan 2012 10:21
Last modified: 18 Jul 2017 10:48

Export record

Contributors

Author: Kannan Kankeyanathan
Thesis advisor: Jacek Brodzki

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×