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Amenability of Closed Subgroups and Orlicz Spaces (1305.6828v3)
Published 29 May 2013 in math.RT and math.FA
Abstract: We prove that a closed subgroup $H$ of a second countable locally compact group $G$ is amenable if and only if its left regular representation on an Orlicz space $L\Phi(G)$ for some $\Delta_2$-regular $N$-function $\Phi$ almost has invariant vectors. We also show that a noncompact second countable locally compact group $G$ is amenable if and ony if the first cohomology space $H1(G,L\Phi(G))$ is non-Hausdorff for some $\Delta_2$-regular $N$-function $\Phi$.