Character amenability of the intersection of Lipschitz algebras

Abstract

Let (X, d) bea metric space and let J ⊆ [0, ∞) be nonempty. We study the structure of the arbitrary intersections of Lipschitz algebras and define a special Banach subalgebra of ∩y∈j Lipy X, denoted by ILipj X. Mainly, we investigate the C-character amenability of ILipj 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 ILipj X, specially Lipschitz algebras, under an additional assumption. © Canadian Mathematical Society 2017.