[Banach] Abstract of a paper by Christian Rosendal

This is an announcement for the paper "Rigidity of commuting affine actions on reflexive Banach spaces" by Christian Rosendal.

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.

Archive classification: math.GR math.FA

Submitted from: rosendal.math@gmail.com

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

http://front.math.ucdavis.edu/1207.3731

or

http://arXiv.org/abs/1207.3731