A generalization of amenability and inner amenability of groups

Ali Ghaffari

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 3, page 729-742
  • ISSN: 0011-4642

Abstract

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Let G be a locally compact group. We continue our work [A. Ghaffari: Γ -amenability of locally compact groups, Acta Math. Sinica, English Series, 26 (2010), 2313–2324] in the study of Γ -amenability of a locally compact group G defined with respect to a closed subgroup Γ of G × G . In this paper, among other things, we introduce and study a closed subspace A Γ p ( G ) of L ∞ ( Γ ) and then characterize the Γ -amenability of G using A Γ p ( G ) . Various necessary and sufficient conditions are found for a locally compact group to possess a Γ -invariant mean.

How to cite

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Ghaffari, Ali. "A generalization of amenability and inner amenability of groups." Czechoslovak Mathematical Journal 62.3 (2012): 729-742. <http://eudml.org/doc/246466>.

@article{Ghaffari2012,
abstract = {Let $G$ be a locally compact group. We continue our work [A. Ghaffari: $\Gamma $-amenability of locally compact groups, Acta Math. Sinica, English Series, 26 (2010), 2313–2324] in the study of $\Gamma $-amenability of a locally compact group $G$ defined with respect to a closed subgroup $\Gamma $ of $G\times G$. In this paper, among other things, we introduce and study a closed subspace $A_\Gamma ^p(G)$ of $L^\infty (\Gamma )$ and then characterize the $\Gamma $-amenability of $G$ using $A_\Gamma ^p(G)$. Various necessary and sufficient conditions are found for a locally compact group to possess a $\Gamma $-invariant mean.},
author = {Ghaffari, Ali},
journal = {Czechoslovak Mathematical Journal},
keywords = {amenability; Banach algebra; inner amenability; locally compact group; amenability; Banach algebra; inner amenability; locally compact group},
language = {eng},
number = {3},
pages = {729-742},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A generalization of amenability and inner amenability of groups},
url = {http://eudml.org/doc/246466},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Ghaffari, Ali
TI - A generalization of amenability and inner amenability of groups
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 3
SP - 729
EP - 742
AB - Let $G$ be a locally compact group. We continue our work [A. Ghaffari: $\Gamma $-amenability of locally compact groups, Acta Math. Sinica, English Series, 26 (2010), 2313–2324] in the study of $\Gamma $-amenability of a locally compact group $G$ defined with respect to a closed subgroup $\Gamma $ of $G\times G$. In this paper, among other things, we introduce and study a closed subspace $A_\Gamma ^p(G)$ of $L^\infty (\Gamma )$ and then characterize the $\Gamma $-amenability of $G$ using $A_\Gamma ^p(G)$. Various necessary and sufficient conditions are found for a locally compact group to possess a $\Gamma $-invariant mean.
LA - eng
KW - amenability; Banach algebra; inner amenability; locally compact group; amenability; Banach algebra; inner amenability; locally compact group
UR - http://eudml.org/doc/246466
ER -

References

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