The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces

Ya A. Kopylov

doi:10.1134/S0037446618060125

The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces

Ya A. Kopylov

Кафедра математического анализа ММФ

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

Аннотация

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 π_Φ of G on the unit sphere of the Orlicz space L^Φ(G/H) for some N-function Φ ∈ Δ₂ satisfies the Rao–Reiter condition (P_Φ).

Язык оригинала	английский
Страницы (с-по)	1094-1099
Число страниц	6
Журнал	Siberian Mathematical Journal
Том	59
Номер выпуска	6
DOI	https://doi.org/10.1134/S0037446618060125
Состояние	Опубликовано - 1 ноя 2018

Доступ к документу

10.1134/S0037446618060125

Другие файлы и ссылки

Link to publication in Scopus

Цитировать

@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.}",

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",

}

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 -

The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces

Аннотация

Доступ к документу

Другие файлы и ссылки

Fingerprint

Цитировать