Rigidity of commuting affine actions on reflexive Banach spaces
Group Theory
2012-07-17 v1 Functional Analysis
Abstract
We give a simple argument to show that if {\alpha} is an affine isometric action of a product G x H of topological groups on a reflexive Banach space X with linear part {\pi}, then either {\pi}(H) fixes a unit vector or {\alpha}|G almost fixes a point on X. It follows that any affine isometric action of an abelian group on a reflexive Banach space X, whose linear part fixes no unit vectors, almost fixes points on X.
Keywords
Cite
@article{arxiv.1207.3731,
title = {Rigidity of commuting affine actions on reflexive Banach spaces},
author = {Christian Rosendal},
journal= {arXiv preprint arXiv:1207.3731},
year = {2012}
}