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Permanent link (DOI): https://doi.org/10.7939/R3HD7NZ4N

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Translation operators on group von Neumann algebras and Banach algebras related to locally compact groups Open Access

Descriptions

Other title
Subject/Keyword
Banach algebras
Translation invariant means
Locally compact groups
Group von Neumann algebras
Translation operators
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Cheng, Yin-Hei
Supervisor and department
Lau, Anthony To-Ming (Mathematics and Statistical Sciences)
Examining committee member and department
Dai, Feng (Mathematics and Statistical Sciences)
Al-Hussein, Mohamed (Construction Engineering and Management)
Derighetti, Antoine (Institut de Mathématiques, Université de Lausanne)
Troitsky, Vladimir G. (Mathematics and Statistical Sciences)
Runde, Volker (Mathematics and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization

Date accepted
2010-08-26T21:39:41Z
Graduation date
2010-11
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
Let $G$ be a locally compact group, $G^*$ be the set of all extreme points of the set of normalized continuous positive definite functions of $G$ and $a(G)$ be the closed subalgebra generated by $G^*$ in $B(G)$. When $G$ is abelian, $G^*$ is the set of dirac measures of the dual group of $G$. The general properties of $G^*$ are investigated in this thesis. We study the properties of $a(G)$, particularly on its spectrum. We also define translation operators on $VN(G)$ via $G^*$ and investigate the problem of the existence of translation means on $VN(G)$ which are not topological invariant. Lastly, we define reflexivity of subgroups of $G$ by using $G^*$, and show that a subgroup $H$ is reflexive if and only if $G$ had $H$-separation property. If $G$ is abelian, there is correspondence between closed subgroups of $G$ and closed subgroups of the dual group $\hat{G}$. We generalize this result to the class of groups having separation property.
Language
English
DOI
doi:10.7939/R3HD7NZ4N
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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