Characterizations of amenable representations of locally compact groups

被引：0

作者：

Cheng, Michael Yin-Hei ^{[1
]}

机构：

[1] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada

来源：

STUDIA MATHEMATICA | 2012年 / 213卷 / 03期

关键词：

Fourier algebras; Fourier-Stieltjes algebras; locally compact groups; amenability; approximate identity; factorization; weak closure; von-Neumann algebras;

D O I：

10.4064/sm213-3-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a locally compact group and let it be a unitary representation. We study amenability and H-amenability of it in terms of the weak closure of (pi circle times pi) (G) and factorization properties of associated coefficient subspaces (or subalgebras) in B(G). By applying these results, we obtain some new characterizations of amenable groups.

引用

页码：207 / 225

页数：19

共 17 条

[1]

[Anonymous], 1988, MATH SURVEYS MONOGR

[2]

[Anonymous], VAN NOSTRAND MATH ST

[3]

[Anonymous], 1964, Bull. Soc. Math. France, DOI DOI 10.24033/BSMF.1607

[4]

[Anonymous], 1977, North-Holland Mathematical Library

[5]

[Anonymous], 1995, STUD ADV MATH

[6]

Arsac G., 1976, PUBL DEP MATH LYON, V13, P1

[7] AMENABLE UNITARY REPRESENTATIONS OF LOCALLY COMPACT-GROUPS [J].

BEKKA, MEB .

INVENTIONES MATHEMATICAE, 1990, 100 (02) :383-401

[8] The weak closure of the set of left translation operators [J].

Chou, C ;

Xu, GW .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (02) :465-471

[9] Vector-valued invariant means on spaces of bounded operators associated to a locally compact group [J].

Chou, C ;

Lau, ATM .

ILLINOIS JOURNAL OF MATHEMATICS, 2001, 45 (02) :581-602

[10] NONFACTORIZATION IN COMMUTATIVE, WEAKLY SELF-ADJOINT BANACH ALGEBRAS [J].

FEICHTINGER, HG ;

GRAHAM, CC ;

LAKIEN, EH .

PACIFIC JOURNAL OF MATHEMATICS, 1979, 80 (01) :117-125

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