• Corpus ID: 119567068

# Amenability of Closed Subgroups and Orlicz Spaces

@article{Kopylov2013AmenabilityOC,
title={Amenability of Closed Subgroups and Orlicz Spaces},
author={Yaroslav Kopylov},
journal={arXiv: Representation Theory},
year={2013}
}
• Y. Kopylov
• Published 29 May 2013
• Mathematics
• arXiv: Representation Theory
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 $\Phi$.
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