Approximate essential character amenability of Banach algebras

Let A be a Banach algebra and ' be a character on A. The notions of approximate essential '-amenability and approximate essential character '-amenability of A are introduced and some properties of such algebras are investigated. Then by means of some examples the distinctions between this new notions and essentially -amenability for A are shown.

Pseudo-amenability and pseudo-contractibility of restricted semigroup algebra

In this article the pseudo-amenability and pseudo-contractibility of restricted semigroup algebra $l_r^1(S)$ and semigroup algebra, l1(Sr) on restricted semigroup, Sr are investigated for different classes of inverse semi-groups such as Brandt semigroup, and Clifford semigroup. We particularly show the equivalence between pseudo-amenability and character amenability of restricted semigroup algebra on a Clifford semigroup and semigroup algebra on a restricted semigroup. Moreover, we show that when S = M0(G, I)is a Brandt semigroup, pseudo-amenability of l1(Sr) is equivalent to its pseudo-contractibility.

ϕ-amenability and character amenability of Fréchet algebras

Right φ-amenability and right character amenability have been introduced for Banach algebras. Here, these concepts will be generalized for Fréchet algebras. Then some of the previous available results about right φ-amenability and right character amenability for the case of Banach algebras will be verified for Fréchet algebras. Related results about Segal Fréchet algebras are provided.

Module amenability, module character biprojectivity and module character biflatness of lau product of two Banach algebras

Let A be a Banach algebra and T be an U-module homomorphism from U-bimodule B into U-bimodule A. We investigate module amenability (resp. module approximate amenability), module character amenability (resp. module character approximate amenability), module character biprojectivity and module character biflatness of A x Tu B for every two Banach U-bimodule A and B.

Character Amenability of the Intersection of Lipschitz Algebras

Let (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.