On a question of Kazhdan and Yom Din

TL;DR

This paper investigates a question posed by Kazhdan and Yom Din, establishing new fixed point theorems for group actions on dual Banach spaces and concluding the answer to their question is negative.

Contribution

The paper introduces novel fixed point theorems for linear group actions on dual Banach spaces and resolves the question of Kazhdan and Yom Din negatively.

Findings

New fixed point theorems for linear actions on dual Banach spaces

The answer to Kazhdan and Yom Din's question is negative in general

Provides insights into group actions on Banach spaces

Abstract

Studying a question of Kazhdan and Yom Din we first prove some new 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.