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Permanent link (DOI): https://doi.org/10.7939/R31J97K0M

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Separation properties and the group von Neumann algebra Open Access

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Other title
Subject/Keyword
group von Neumann algebra
Fourier algebra
adapted probability measure
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Tanko, Zsolt
Supervisor and department
Runde, Volker (Mathematical and Statistical Sciences)
Examining committee member and department
Gannon, Terry (Mathematical and Statistical Sciences)
Gille, Stefan (Mathematical and Statistical Sciences)
Runde, Volker (Mathematical and Statistical Sciences)
Tomczak-Jaegermann, Nicole (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2016-05-11T09:34:37Z
Graduation date
2016-06
Degree
Master of Science
Degree level
Master's
Abstract
A group endowed with a topology compatible with the group operations and for which every point has a neighborhood contained in a compact set is called a locally compact group. On such groups, there is a canonical translation invariant Borel measure that one may use to define spaces of p-integrable functions. With this structure at hand, abstract harmonic analysis further associates to a locally compact group various algebras of functions and operators. We study the capacity these algebras to distinguish closed subgroups of a locally compact group. We also characterize an operator algebraic property of von Neumann algebras associated to a locally compact group. Our investigations lead to a concise argument characterizing cyclicity of the left regular representation of a locally compact group.
Language
English
DOI
doi:10.7939/R31J97K0M
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 (Portable Document Format)
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Last modified: 2016:11:16 15:44:59-07:00
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File title: 1 Introduction and overview
File title: Separation properties and the group von Neumann algebra
File author: Zsolt Tanko
Page count: 74
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