Character Amenability of the Intersection of Lipschitz Algebras

Abtahi, Fatemeh ; Azizi, Mohsen ; Rejali, Ali

Canadian mathematical bulletin, Tome 60 (2017) no. 4, pp. 673-689

Résumé

Let $(X,d)$ be a metric space and let $J\subseteq [0,\infty )$ be nonempty. We study the structure of the arbitrary intersections of Lipschitz algebras and define a special Banach subalgebra of ${{\cap }_{\gamma \in J\,}}\text{Li}{{\text{p}}_{\gamma \,}}X$ , denoted by $\text{ILi}{{\text{p}}_{J}}X$ . Mainly, we investigate the $C$ -character amenability of $\text{ILi}{{\text{p}}_{J}}X$ , in particular Lipschitz algebras. We address a gap in the proof of a recent result in this field. Then we remove this gap and obtain a necessary and sufficient condition for $C$ -character amenability of $\text{ILi}{{\text{p}}_{J}}X$ , specially Lipschitz algebras, under an additional assumption.

Détail

DOI : 10.4153/CMB-2017-039-8

Mots-clés : 46H050, 46J10, 11J83, amenability, character amenability, Lipschitz algebra, metric space