Beurling algebras and uniform norms

$sigma$-Connes Amenability and Pseudo-(Connes) Amenability of Beurling Algebras

In this paper,  pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.

On the Beurling Algebras A+α(d)—derivations and Extensions

Based on a description of the squares of cofinite primary ideals of A + α (D), we prove the following results: for α ≥ 1, there exists a derivation from A + α (D) into a finite-dimensional module such that this derivation is unbounded on every dense subalgebra; for m ∈ N and α ∈ [m, m + 1), every finite-dimensional extension of A + α (D) splits algebraically if and only if α ≥ m + 1/2.

Weak Amenability and 2-weak Amenability of Beurling Algebras

Let Lω(G) be a Beurling algebra on a locally compact abelian group G. We look for general conditions on the weight which allows the vanishing of continuous derivations of Lω(G). This leads us to introducing vector-valued Beurling algebras and considering the translation of operators on them. This is then used to connect the augmentation ideal to the behavior of derivation space. We apply these ...

On the Beurling algebras A+α(𝔻)derivations and extensions

M-IDEAL STRUCTURE IN UNIFORM ALGEBRAS

It is proved that if A is aregular uniform algebra on a compact Hausdorff space X in which every closed ideal is an M-ideal, then A = C(X).