Geodesic
Amenability of Closed Subgroups and Orlicz Spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 583-590

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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 $H^1(G,L^\Phi(G))$ is non-Hausdorff for some $\Delta_2$-regular $N$-function $\Phi$.
Keywords: locally compact group, second countable group, closed subgroup, $N$-function, Orlicz space, 1-cohomology.
Mots-clés : amenable group 
@article{SEMR_2013_10_a32,
     author = {Ya A. Kopylov},
     title = {Amenability of {Closed} {Subgroups} and {Orlicz} {Spaces}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {583--590},
     publisher = {mathdoc},
     volume = {10},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a32/}
}
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Ya A. Kopylov. Amenability of Closed Subgroups and Orlicz Spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 583-590. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a32/