Equicontinuous actions of semisimple groups

  • Uri Bader

    Technion - Israel Institute of Technology, Haifa, Israel
  • Tsachik Gelander

    The Weizmann Institute of Science, Rehovot, Israel


We study equicontinuous actions of semisimple groups and some generalizations. We prove that any such action is universally closed, and in particular proper. We derive various applications, both old and new, including closedness of continuous homomorphisms, nonexistence of weaker topologies, metric ergodicity of transitive actions and vanishing of matrix coefficients for reflexive (more generally: WAP) representations.

Cite this article

Uri Bader, Tsachik Gelander, Equicontinuous actions of semisimple groups. Groups Geom. Dyn. 11 (2017), no. 3, pp. 1003–1039

DOI 10.4171/GGD/420