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.

引用

页码：465 / 471

页数：7

共 13 条

[1] ON THE C-ASTERISK-ALGEBRA GENERATED BY THE LEFT REGULAR REPRESENTATION OF A LOCALLY COMPACT GROUP [J].