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The weak closure of the set
of left translation operators


Authors: Ching Chou and Guangwu Xu
Journal: Proc. Amer. Math. Soc. 127 (1999), 465-471
MSC (1991): Primary 43A30, 46A50, 46L10; Secondary 43A07, 43A46, 46L05
DOI: https://doi.org/10.1090/S0002-9939-99-04537-2
MathSciNet review: 1468187
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Abstract: It is known that for an amenable locally compact group $G$, $0$ is not in the weak closure of $\{ \lambda (g) : g \in G \}$ of $VN(G)$. In this paper, it is proved that the converse of this is true. In other words, if $G$ is a non-amenable locally compact group, then $0$ is in the weak closure of $\{ \lambda (g) : g \in G \}$. This answers several questions of Ülger. Applications to the algebra $C^{*}_{\delta }(G)$ and the dual of the reduced group $C^{*}$-algebra are obtained.


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Additional Information

Ching Chou
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14214
Email: MTHCHOU@acsu.buffalo.edu

Guangwu Xu
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 1G2
Email: xu@vega.math.ualberta.ca

DOI: https://doi.org/10.1090/S0002-9939-99-04537-2
Keywords: Weak closure, von Neumann algebras, Fourier algebras, amenable groups
Received by editor(s): January 20, 1997
Received by editor(s) in revised form: May 21, 1997
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1999 American Mathematical Society

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