Abstract
Let X be a proper hyperbolic geodesic metric space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is not elementary then for every p ∈ (1, ∞) the second continuous bounded cohomology group H2 cb (G, L p (G)) does not vanish. As an application, we derive some structure results for closed subgroups of Iso(X).
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