This is an announcement for the paper "On isometry groups and maximal symmetry" by Valentin Ferenczi and Christian Rosendal.

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.

Archive classification: math.FA math.LO

Mathematics Subject Classification: Primary: 22F50, 46B03, 46B04. Secondary: 03E15

Submitted from: rosendal@math.uic.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1106.5020

or

http://arXiv.org/abs/1106.5020