Proper cocycles and weak forms of amenability

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 ...

Amenability and Weak Amenability of Triangular Banach Algebras

Amenability and weak amenability of l-algebras of polynomial hypergroups

We investigate amenability and weak amenability of the l1-algebra of polynomial hypergroups. We derive conditions for (weak) amenability adapted to polynomial hypergroups and show that these conditions are often not satisfied. However, for the hypergroup induced by Chebyshev polynomials of the first kind we prove amenability.

2n-Weak module amenability of semigroup algebras

‎Let $S$ be an inverse semigroup with the set of idempotents $E$‎. We prove that the semigroup algebra $ell^{1}(S)$ is always‎ ‎$2n$-weakly module amenable as an $ell^{1}(E)$-module‎, ‎for any‎ ‎$nin mathbb{N}$‎, ‎where $E$ acts on $S$ trivially from the left‎ ‎and by multiplication from the right‎. ‎Our proof is based on a common fixed point property for semigroups‎.  

Homomorphism Weak amenability of certain Banach algebras

In this paper we introduce the notion of $varphi$-commutativity for a Banach algebra $A$, where $varphi$ is a continuous homomorphism on $A$ and study the concept of $varphi$-weak amenability for $varphi$-commutative Banach algebras. We give an example to show that the class of $varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We charac...