An example of a non-commutative uniform Banach group

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Doucha, Michal¹ 

[1] Polish Acad Sci, Inst Math, PL-00656 Warsaw, Poland

关键词: Uniform Banach group;    Free group;    Hilbert's fifth problem;    Lipschitz-free space;   

DOI  :  10.1016/j.jmaa.2016.08.034

来源: Elsevier

【 摘 要 】

Benyamini and Lindenstrauss mention in their monograph (Benyamini and Lindenstrauss, 2000 [2]) that there is no known example of a non-commutative uniform Bannrh group. Prassidis and Weston also asked whether there is a non-commutative example. We answer this problem affirmatively. We construct a non-commutative uniform Banach group which has the free group of countably many generators as a dense subgroup. Moreover, we show that our example is a free one-generated uniform Banach group whose metric induced by the norm is bi-invariant. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free