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.
- Howe-Moore Theorem
- Mautner's phenomenon
- Metric ergodicity
- Uniform structures
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Discrete Mathematics and Combinatorics