Essential Character Amenability of Banach Algebras

Abstract

For a Banach algebra A and a character φ on A, we introduce and study the notion of essential φ-amenability of A. We give some examples to show that the class of essentially φ-amenable Banach algebras is larger than that of φ-amenable Banach algebras introduced by Kaniuth et al. ['On φ-amenability of Banach algebras', Math. Proc. Cambridge Philos. Soc. 144 (2008), 85-96]. Finally, we characterize the essential φ-amenability of various Banach algebras related to locally compact groups.2010 Mathematics subject classification: primary 43A07, 46H05; secondary 43A20.

Approximate essential character amenability of Banach algebras

“…We start this section with a definition, which is variant of the concept of essential character amenability by Nasr-Isfahani and Nemati in [9]. Definition 2.1.…”

“…The concepts of approximate left and right character amenability for Banach algebras were introduced in [1] and also another versions of character amenability of Banach algebras, called module character amenability and module approximate character amenability of Banach algebras were introduced and studied in [2,3]. Meanwhile, the concept of essentially ϕ-amenable for a Banach algebra which ϕ ∈ σ(A) ∪ {0}, was introduced by Nasr-Isfahani and Nemati in [9]. In this paper, the subjects of [9] will be extended, i.e., we introduce the notions of approximate essential (ϕ, A)-amenability and approximate essential character amenability for Banach algebras and obtain some properties of such algebras.…”

“…Meanwhile, the concept of essentially ϕ-amenable for a Banach algebra which ϕ ∈ σ(A) ∪ {0}, was introduced by Nasr-Isfahani and Nemati in [9]. In this paper, the subjects of [9] will be extended, i.e., we introduce the notions of approximate essential (ϕ, A)-amenability and approximate essential character amenability for Banach algebras and obtain some properties of such algebras.…”

On $Δ$-weak $ϕ$-amenability of Banach algebras

“…With this product X is a Banach algebra which we denote it by A φ (X). It is clear that ∆(A φ (X)) = {φ} and A φ (X) is φ-amenable if and only if dim(X) = 1 [16,Example 2.4].…”

Some Characterizations of Character Amenable Banach Algebras

“…Similar to the amenability of Banach algebras, versions of CA such as character contractibility and essential character amenability, have been defined and studied (see [2,11,19]). Moreover, new results related to CA of Banach algebras have been reported in [17].…”