Some Characterizations of Character Amenable Banach Algebras

Abstract

Abstract. In this study, the character amenability of Banach algebras is considered and some characterization theorems are established. Indeed, we prove that the character amenability of Lipschitz algebras is equivalent to that of Banach algebras.

Frechet algebras in abstract Harmonic analysis

“…[59, Proposition 2.2.1]. In recent years, a large number of papers concerning amenability of Banach algebras have appeared; see for instance [5,12,18,28,29,32,44]. In [49], the arguments above have generalized as follows: G 3.1.…”

φ-contractibility of some classes of Banach function algebras

“…Also, when X is a compact plane set we simply write Lip(X, α) and ip(X, α) instead of Lip(X, | · | α ) and ip(X, | · | α ), respectively. For a compact metric space (X, d), ϕ-amenability of the Lipschitz algebras Lip(X, d α ) and ip(X, d α ) have been studied by Kaniuth et al in [14,Example 5.3], (see also [8,Theorem 2.4]). Recently, Dashti et al in [7] characterized ϕ-amenability of Lip(X, d α ), where (X, d) is a locally compact metric space.…”