The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces

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The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces. / Kopylov, Ya A.

In: Siberian Mathematical Journal, Vol. 59, No. 6, 01.11.2018, p. 1094-1099.

Research output: Contribution to journal › Article › peer-review

Harvard

Kopylov, YA 2018, 'The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces', Siberian Mathematical Journal, vol. 59, no. 6, pp. 1094-1099. https://doi.org/10.1134/S0037446618060125

APA

Kopylov, Y. A. (2018). The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces. Siberian Mathematical Journal, 59(6), 1094-1099. https://doi.org/10.1134/S0037446618060125

Vancouver

Kopylov YA. The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces. Siberian Mathematical Journal. 2018 Nov 1;59(6):1094-1099. doi: 10.1134/S0037446618060125

Author

Kopylov, Ya A. / The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces. In: Siberian Mathematical Journal. 2018 ; Vol. 59, No. 6. pp. 1094-1099.

BibTeX

@article{6924fb1438dc48999dea1f8938c18757,

title = "The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces",

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 πΦ of G on the unit sphere of the Orlicz space LΦ(G/H) for some N-function Φ ∈ Δ2 satisfies the Rao–Reiter condition (PΦ).",

keywords = "amenability, homogeneous space, locally compact group, N-function, Orlicz space, Δ-condition, Delta(2)-condition",

author = "Kopylov, {Ya A.}",

note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Ltd.",

year = "2018",

month = nov,

day = "1",

doi = "10.1134/S0037446618060125",

language = "English",

volume = "59",

pages = "1094--1099",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",

number = "6",

}

RIS

TY - JOUR

T1 - The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces

AU - Kopylov, Ya A.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - 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 πΦ of G on the unit sphere of the Orlicz space LΦ(G/H) for some N-function Φ ∈ Δ2 satisfies the Rao–Reiter condition (PΦ).

AB - 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 πΦ of G on the unit sphere of the Orlicz space LΦ(G/H) for some N-function Φ ∈ Δ2 satisfies the Rao–Reiter condition (PΦ).

KW - amenability

KW - homogeneous space

KW - locally compact group

KW - N-function

KW - Orlicz space

KW - Δ-condition

KW - Delta(2)-condition

UR - http://www.scopus.com/inward/record.url?scp=85059771141&partnerID=8YFLogxK

U2 - 10.1134/S0037446618060125

DO - 10.1134/S0037446618060125

M3 - Article

AN - SCOPUS:85059771141

VL - 59

SP - 1094

EP - 1099

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 6

ER -

ID: 18119297