Weak amenability of Coxeter groups
نویسنده
چکیده
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,S) un groupe de Coxeter. Nous construisons une extension, au disque unité ouvert, de la série des représentations unitaires associées aux fonctions definies positives g 7→ rl(g). (Ici, 0 < r < 1, et l désigne la fonction longueur par rapport aux générateurs S.) Les représentations ainsi construites sont uniformément bornées et nous démontrons que ceci implique que le groupe G est faiblement moyenable. Acknowledgements : Part of this work has been done while the author visited the Mathematical Institute of the University of Wroc law in 1998. AMS Mathematical Subject Classification(1991): 22D15, 43A65, 46H99, 46L99
منابع مشابه
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.
متن کاملWeak and $(-1)$-weak amenability of second dual of Banach algebras
For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')={0}$. In this paper, among other things, we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^ast$-algebra is $(-1)$-Weakly amenable.
متن کاملClosed Ideals, Point Derivations and Weak Amenability of Extended Little Lipschitz Algebras
...
متن کاملThe structure of ideals, point derivations, amenability and weak amenability of extended Lipschitz algebras
Let $(X,d)$ be a compactmetric space and let $K$ be a nonempty compact subset of $X$. Let $alpha in (0, 1]$ and let ${rm Lip}(X,K,d^ alpha)$ denote the Banach algebra of all continuous complex-valued functions $f$ on$X$ for which$$p_{(K,d^alpha)}(f)=sup{frac{|f(x)-f(y)|}{d^alpha(x,y)} : x,yin K , xneq y}
متن کامل