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Permanent link (DOI): https://doi.org/10.7939/R34F1MZ2X

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Operator amenability of ultrapowers of the Fourier algebra Open Access

Descriptions

Other title
Subject/Keyword
ultra-operator amenability
ultra-amenability
fourier algebra
ultrapowers
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Schlitt, Kyle J
Supervisor and department
Volker Runde (Mathematics)
Examining committee member and department
Douglas Farenick (Mathematics)
Vladimir Troitsky (Mathematics)
Jochen Kuttler (Mathematics)
Alexander Litvak (Mathematics)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2017-09-26T14:38:49Z
Graduation date
2017-11:Fall 2017
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
It has been shown by Matthew Daws that the group algebra of a discrete group is never ultra-amenable. We explore the weak analogue to this statement and demonstrate that if any commutative group algebra is ultra-weakly amenable, then the underlying group must necessarily be discrete. By showing that ultrapowers of complete maximal operator spaces are themselves maximal, we are able to demonstrate that the assumption of ultra-operator amenability of the Fourier algebra A(G) forces G to be discrete. By considering a wide class of discrete groups, we find sufficient evidence to make reasonable the conjecture that such a property may well force G to be finite. We conclude with consideration of another weak analogue, showing that ultra-weak operator amenability of A(G) already forces G to be discrete.
Language
English
DOI
doi:10.7939/R34F1MZ2X
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
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File format: pdf (PDF/A)
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Last modified: 2017:11:08 17:09:12-07:00
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File title: Operator Amenability of Ultrapowers of the Fourier Algebra
File author: Kyle Schlitt
Page count: 66
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