APPROXIMATE WEAK AMENABILITY OF I0(SL(2,ℝ))

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

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...

Module approximate amenability of Banach algebras

In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...