The weak closure of the set of left translation operators

被引：9
|
作者：
Chou, C [1 ]
Xu, GW
机构：
[1] SUNY Buffalo, Dept Math, Buffalo, NY 14214 USA
[2] Univ Alberta, Dept Math Sci, Edmonton, AB T6G 1G2, Canada
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1999年 / 127卷 / 02期
关键词：
weak closure; von Neumann algebras; Fourier algebras; amenable groups;
D O I：
10.1090/S0002-9939-99-04537-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is known that for an amenable locally compact group G, 0 is not in the weak closure of {lambda(g) : g is an element of 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 is an element of G}. This answers several questions of Ulger. Applications to the algebra C-delta*(G) and the dual of the reduced group C*-algebra are obtained.
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页码：465 / 471
页数：7
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