Character Amenability of the Intersection of Lipschitz Algebras

Abstract

AbstractLet (X, d) be ametric space and letJ⊆ [0,∞) be nonempty. We study the structure of the arbitrary intersections of Lipschitz algebras and define a special Banach subalgebra of ∩y∊JLipyX, denoted by ILipJX. Mainly, we investigate theC-character amenability of ILipJX, 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 suõcient condition forC-character amenability of ILipJX, specially Lipschitz algebras, under an additional assumption.