Kazhdan projections, random walks and ergodic theorems

Author: 

Druţu, C
Nowak, P

Publication Date: 

18 January 2017

Journal: 

Journal für die reine und angewandte Mathematik (Crelles Journal)

Last Updated: 

2019-04-18T08:23:16.193+01:00

DOI: 

10.1515/crelle-2017-0002

abstract: 

<jats:title>Abstract</jats:title><jats:p>In this paper we investigate generalizations of Kazhdan’s property (T) to the setting of uniformly convex Banach spaces. We explain the interplay between the existence of spectral gaps and that of Kazhdan projections. Our methods employ Markov operators associated to a random walk on the group, for which we provide new norm estimates and convergence results. This construction exhibits useful properties and flexibility, and allows to view Kazhdan projections in Banach spaces as natural objects associated to random walks on groups.</jats:p><jats:p>We give a number of applications of these results. In particular, we address several open questions. We give a direct comparison of properties (TE) and F</jats:p>

Symplectic id: 

685467

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article