An example of a non-commutative uniform Banach group
Functional Analysis
2015-08-18 v2 General Topology
Group Theory
Abstract
Benyamini and Lindenstrauss mention in their monograph \emph{Geometric nonlinear functional analysis Vol. 1., American Mathematical Society Colloquium Publications, 48. American Mathematical Society, Providence, RI, 2000} that there is no known example of a non-commutative uniform Banach 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.
Keywords
Cite
@article{arxiv.1504.05841,
title = {An example of a non-commutative uniform Banach group},
author = {Michal Doucha},
journal= {arXiv preprint arXiv:1504.05841},
year = {2015}
}
Comments
The second version is extended with few new results