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15 July 2013 On isometry groups and maximal symmetry
Valentin Ferenczi, Christian Rosendal
Duke Math. J. 162(10): 1771-1831 (15 July 2013). DOI: 10.1215/00127094-2322898

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.

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Valentin Ferenczi. Christian Rosendal. "On isometry groups and maximal symmetry." Duke Math. J. 162 (10) 1771 - 1831, 15 July 2013. https://doi.org/10.1215/00127094-2322898

Information

Published: 15 July 2013
First available in Project Euclid: 11 July 2013

zbMATH: 1284.46010
MathSciNet: MR3079260
Digital Object Identifier: 10.1215/00127094-2322898

Subjects:
Primary: 22F50
Secondary: 03E15 , 46B03 , 46B04

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 10 • 15 July 2013
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