43A07 — 3 articles found.
Sur les espaces test pour la moyennabilité
Yousef Al-Gadid, Department of Mathematics, Faculty of Science, Al-Fateh University, Tripoli-Lybie; email: yousef algadid@yahoo.com
Brice R. Mbombo, Departement de Mathematiques, Faculte des Sciences, Universite de Yaounde I, BP 812 Yaounde, Cameron; emaill: bricero@yahoo.fr
Vladimir G. Pestov, Departement de Mathematiques et Statistiques, Universit ́e d’Ottawa, 585, av. King Edward, Ottawa, Ontario, Canada, K1N 6N5; email: vpest283@uottawa.ca
Abstract/Résumé:
We observe that a Polish group \(G\) is amenable if and only if every continuous action of \(G\) on the Hilbert cube admits an invariant probability measure. This generalizes a result of Bogatyi and Fedorchuk. We also show that actions on the Cantor space can be used to detect amenability and extreme amenability of Polish nonarchimedean groups as well as amenability at infinity of discrete countable groups. As corollary, the latter property can also be tested by actions on the Hilbert cube. These results generalize a criterion due to Giordano and de la Harpe.
Nous observons qu’un groupe polonais \(G\) est moyennable si et seulement si toute action continue de \(G\) sur le cube de Hilbert possède une mesure de probabilité invariante. Cela généralise un résultat de Bogatyi et Fedorchuk. Nous démontrons également que les actions continues sur l’espace de Cantor permettent de tester la moyennabilité, la moyennabilité extrême des groupes polonais non archimédiens, et la moyennabilité à l’infini des groupes discrets dénombrables. Il en résulte que cette dernière propriété peut également être testée par les actions sur le cube de Hilbert. Ces résultats généralisent un critère de Giordano et de la Harpe.
Keywords:
AMS Subject Classification:
Means on groups; semigroups; etc.; amenable groups
43A07
PDF(click to download): Sur les espaces test pour la moyennabilité
On co-amenability for groups and von Neumann algebras
N. Monod / S. Popa
Abstract/Résumé:
No abstract available but the full text pdf may be downloaded at the title link below.
Keywords:
AMS Subject Classification:
Means on groups; semigroups; etc.; amenable groups, Analysis on homogeneous spaces,
43A07, 43A85, 46L
PDF(click to download): On co-amenability for groups and von Neumann algebras
On some questions of Eymard and Bekka concerning amenability of homogeneous spaces and induced representations
V. Pestov
Abstract/Résumé:
No abstract available but the full text pdf may be downloaded at the title link below.
Keywords:
AMS Subject Classification:
Induced representations, Means on groups; semigroups; etc.; amenable groups, Representations of groups; semigroups; etc., Analysis on homogeneous spaces
22D30, 43A07, 43A65, 43A85
PDF(click to download): On some questions of Eymard and Bekka concerning amenability of homogeneous spaces and induced representations