2 M ay 2 01 7 Locally compact groups with every isometric action bounded or proper Romain TESSERA and Alain VALETTE
نویسنده
چکیده
A locally compact group G has property PL if every isometric G-action either has bounded orbits or is (metrically) proper. For p > 1, say that G has property BPLp if the same alternative holds for the smaller class of affine isometric actions on Lp-spaces. We explore properties PL and BPLp and prove that they are equivalent for some interesting classes of groups: abelian groups, amenable almost connected Lie groups, amenable linear algebraic groups over a local field of characteristic 0. The appendix provides new examples of groups with property PL, including non-linear ones.
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