Property T of group homomorphisms

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:438

Article

Leung, Chi-Wai¹  Ng, Chi-Keung^2,3 

[1] Chinese Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

[2] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

关键词: Locally compact groups;    Property T;    Strong property T;   

DOI  :  10.1016/j.jmaa.2016.02.026

来源: Elsevier

【 摘 要 】

In this article, we define and study property T for continuous homomorphisms between topological groups. If G is a locally compact group, we show that lambda(G) : G -> U(L-2(G)) has property T if and only if either G is compact or G is non amenable. Moreover, the abelianization G(ab) := G/[(G,G) over bar] is compact if and only if every continuous homomorphism from G to any abelian topological group has property T. Moreover, we show that G has property (T, FD) if and only if any continuous homomorphism from G to any compact group has property T. In the case when G is almost connected, the above is also equivalent to the canonical map from G to its Bohr compactification being a quotient map. We also give some new equivalent forms of the strong property T of a locally compact group. As a consequence, if G is a second countable and has strong property T and H is a closed subgroup of G, there exist at most one G-invariant mean on G/H. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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