The weak closure of the set of left translation operators

Ching Chou; X. U. Guangwu

doi:10.1090/s0002-9939-99-04537-2

The weak closure of the set of left translation operators

Ching Chou
, X. U. Guangwu

Mathematics

University of Alberta

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

It is known that for an amenable locally compact group G, 0 is not in the weak closure of [λ(g) : g ∈ G} of V N(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 (λ(g) : g ∈ G}. This answers several questions of Ulger. Applications to the algebra C*_δ(G) and the dual of the reduced group C*-algebra are obtained.

Original language	English
Pages (from-to)	465-471
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	127
Issue number	2
DOIs	https://doi.org/10.1090/s0002-9939-99-04537-2
State	Published - 1999

Keywords

Amenable groups
Fourier algebras
Von neumann algebras
Weak closure

Access to Document

10.1090/s0002-9939-99-04537-2

Cite this

@article{97132477a61d4b969bbc18a986d5ea74,

title = "The weak closure of the set of left translation operators",

abstract = "It is known that for an amenable locally compact group G, 0 is not in the weak closure of [λ(g) : g ∈ G\} of V N(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 (λ(g) : g ∈ G\}. This answers several questions of Ulger. Applications to the algebra C*δ(G) and the dual of the reduced group C*-algebra are obtained.",

keywords = "Amenable groups, Fourier algebras, Von neumann algebras, Weak closure",

author = "Ching Chou and Guangwu, \{X. U.\}",

year = "1999",

doi = "10.1090/s0002-9939-99-04537-2",

language = "English",

volume = "127",

pages = "465--471",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "2",

}

TY - JOUR

T1 - The weak closure of the set of left translation operators

AU - Chou, Ching

AU - Guangwu, X. U.

PY - 1999

Y1 - 1999

N2 - It is known that for an amenable locally compact group G, 0 is not in the weak closure of [λ(g) : g ∈ G} of V N(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 (λ(g) : g ∈ G}. This answers several questions of Ulger. Applications to the algebra C*δ(G) and the dual of the reduced group C*-algebra are obtained.

AB - It is known that for an amenable locally compact group G, 0 is not in the weak closure of [λ(g) : g ∈ G} of V N(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 (λ(g) : g ∈ G}. This answers several questions of Ulger. Applications to the algebra C*δ(G) and the dual of the reduced group C*-algebra are obtained.

KW - Amenable groups

KW - Fourier algebras

KW - Von neumann algebras

KW - Weak closure

UR - https://www.scopus.com/pages/publications/22444454730

U2 - 10.1090/s0002-9939-99-04537-2

DO - 10.1090/s0002-9939-99-04537-2

M3 - Article

AN - SCOPUS:22444454730

SN - 0002-9939

VL - 127

SP - 465

EP - 471

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -

The weak closure of the set of left translation operators

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this