Equicontinuous actions of semisimple groups

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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.
Original languageEnglish
Pages (from-to)1003-1039
Number of pages37
JournalGroups Geometry And Dynamics
Issue number3
StatePublished - 2017


  • Howe-Moore Theorem
  • Mautner's phenomenon
  • Metric ergodicity
  • Uniform structures
  • WAP-representations

All Science Journal Classification (ASJC) codes

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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