On isometry groups and maximal symmetry
Functional Analysis
2019-12-19 v1 Logic
Abstract
We study problems of maximal symmetry in Banach spaces. This is done by providing an analysis of the structure of small subgroups of the general linear group GL(X), where X is a separable reflexive Banach space. In particular, we provide the first known example of a Banach space X without any equivalent maximal norm, or equivalently such that GL(X) contains no maximal bounded subgroup. Moreover, this space X may be chosen to be super-reflexive.
Cite
@article{arxiv.1106.5020,
title = {On isometry groups and maximal symmetry},
author = {Valentin Ferenczi and Christian Rosendal},
journal= {arXiv preprint arXiv:1106.5020},
year = {2019}
}