Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

The weak closure of the set of left translation operators

Author(s): Ching Chou; Guangwu Xu
Journal: Proc. Amer. Math. Soc. 127 (1999), 465-471.
MSC (1991): Primary 43A30, 46A50, 46L10; Secondary 43A07, 43A46, 46L05
MathSciNet review: 1468187
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Abstract: It is known that for an amenable locally compact group , is not in the weak closure of $\{ \lambda (g) : g \in G \}$ of . In this paper, it is proved that the converse of this is true. In other words, if is a non-amenable locally compact group, then 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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