# Kazhdan projections, random walks and ergodic theorems

@article{Drutu2019KazhdanPR,
title={Kazhdan projections, random walks and ergodic theorems},
author={Cornelia Drutu and Piotr W. Nowak},
journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
year={2019},
volume={2019},
pages={49 - 86}
}
• Published 14 January 2015
• Mathematics
• Journal für die reine und angewandte Mathematik (Crelles Journal)
Abstract 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…

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