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 | References | Similar Articles | Additional Information

Abstract: It is known that for an amenable locally compact group , is not in the weak closure of 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 . This answers several questions of Ülger. Applications to the algebra and the dual of the reduced group -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