On a question of Kazhdan and Yom Din

Abstract

Studying a question of Kazhdan and Yom Din we first prove some fixed point theorems for linear actions of a discrete countable group G on a dual Banach space V*, and then show that the answer to the question in full generality is in the negative. In an appendix it is shown that the answer is negative also for the Banach space \({\cal B}\left( H \right)\) of bounded linear operators on an infinite-dimensional Hilbert space.