On fixed point property for $L_p$-representations of Kazhdan groups

Abstract

Let $G$ be a topological group with finite Kazhdan set, let $\Omega$ be a standard Borel space and $\mu$ a finite measure on $\Omega$. We prove that for any $p\in [1,\infty )$, any affine isometric action $G\curvearrowright L_p(\Omega ,\mu )$ whose linear part arises from an ergodic measure-preserving action $G\curvearrowright (\Omega ,\mu )$, has a fixed point.

Few minor changes

References in corpus (1)

• Fixed-point spectrum for group actions by affine isometries on Lp-spaces