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The Rao–Reiter criterion for the amenability of homogeneous spaces
Ya. A. Kopylovab a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Abstract:
We prove that a homogeneous space $G/H$, with $G$ a locally compact group and $H$ a closed subgroup of $G$, is amenable in the sense of Eymard–Greenleaf if and only if the quasiregular action $\pi_\Phi$ of $G$ on the unit sphere of the Orlicz space $L^\Phi(G/H)$ for some $N$-function $\Phi\in\Delta_2$ satisfies the Rao–Reiter condition $(P_\Phi)$.
Keywords:
locally compact group, homogeneous space, amenability, $N$-function, Orlicz space, $\Delta_2$-condition.
Received: 14.11.2017
Citation:
Ya. A. Kopylov, “The Rao–Reiter criterion for the amenability of homogeneous spaces”, Sibirsk. Mat. Zh., 59:6 (2018), 1375–1382; Siberian Math. J., 59:6 (2018), 1094–1099
Linking options:
https://www.mathnet.ru/eng/smj3050 https://www.mathnet.ru/eng/smj/v59/i6/p1375
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Abstract page: | 200 | Full-text PDF : | 37 | References: | 29 | First page: | 3 |
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