Amenability and Weak Amenability of the Semigroup Algebra l^1 (〖 S〗_T )

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.  

Weak amenability of (2N)-th dual of a Banach algebra

In this paper by using some conditions, we show that the weak amenability of (2n)-th dual of a Banach algebra A for some $ngeq 1$ implies the weak amenability of A.

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

Module Amenability for Semigroup Algebras

We extend the concept of amenability of a Banach algebra A to the case that there is an extra A -module structure on A, and show that when S is an inverse semigroup with subsemigroup E of idempotents, then A = l(S) as a Banach module over A= l(E) is module amenable iff S is amenable. When S is a discrete group, l(E) = C and this is just the celebrated Johnson’s theorem.

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.