This is an announcement for the paper "Group actions on Banach spaces" by Piotr W. Nowak.

Abstract: Recently there has been growing interest in extending Kazhdan's property (T) to other Banach spaces, but even for such familiar classes as the Lebesgue spaces $L_p$, or even spaces isomorphic to the Hilbert space, this program proved to be challenging. Our goal in this survey is to give a fairly complete account of the recent developments and their applications. We purposely focus only on the case of Banach spaces which are not Hilbert spaces, discussing the latter case mainly as motivation. Wa also discuss metrically proper actions on Banach spaces, their interplay with fixed point properties and geometric applications.

Archive classification: math.GR math.DS math.FA math.OA

Submitted from: pnowak@mimuw.edu.pl

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

http://front.math.ucdavis.edu/1302.6609

or

http://arXiv.org/abs/1302.6609