On isometry groups and maximal symmetry

Details On isometry groups and maximal symmetry On isometry groups and maximal symmetry

2011-06-24

arxiv.org/abs/1106.5020v1

Mathematics

Functional Analysis

Scientific paper

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.

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