Weak amenability is stable under graph products

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 ...

Weak amenability of Coxeter groups

Let (G,S) be a Coxeter group. We construct a continuation, to the open unit disc, of the unitary representations associated to the positive definite functions g 7→ rl(g). (Here 0 < r < 1, and l denotes the length function with respect to the generating set S.) The constructed representations are uniformly bounded and we prove that this implies the weak amenability of the group G. Résumé Soit (G...

Weak Amenability of Hyperbolic Groups

We prove that hyperbolic groups are weakly amenable. This partially extends the result of Cowling and Haagerup showing that lattices in simple Lie groups of real rank one are weakly amenable. We take a combinatorial approach in the spirit of Haagerup and prove that for the word length metric d on a hyperbolic group, the Schur multipliers associated with r have uniformly bounded norms for 0 < r ...

Amenability and Weak Amenability of Triangular Banach Algebras

Weak amenability of Segal algebras

Let G be a locally compact abelian group, and let p 2 1; 1). We show that the Segal algebra S p (G) is always weakly amenable, but that it is amenable only if G is discrete.