On uniqueness of invariant means

被引:24
|
作者
Bekka, MB [1 ]
机构
[1] Univ Metz, Dept Math, F-57045 Metz, France
关键词
invariant means on compact groups; p-adic groups; Selberg inequality; lattices in semisimple Lie groups; linear algebraic groups;
D O I
10.1090/S0002-9939-98-04044-1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The following results on uniqueness of invariant means are shown: (i) Let G be a connected almost simple algebraic group defined over Q. Assume that G(R), the group of the real points in G, is not compact. Let p be a prime, and let G(Z(p)) be the compact p-adic Lie group of the Z(p)-points in G. Then the normalized Haar measure on G(Z(p)) is the unique invariant mean on L-infinity(G(Z(p))). (ii) Let G be a semisimple Lie group with finite centre and without compact factors, and let Gamma be a lattice in G. Then integration against the G-invariant probability measure on the homogeneous space G/Gamma is the unique Gamma-invariant mean on L-infinity(G/Gamma).
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页码:507 / 514
页数:8
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