Weak amenability of commutative Beurling algebras
| Autor: | Zhang, Yong |
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| Rok vydání: | 2012 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For a locally compact Abelian group $G$ and a continuous weight function $\omega$ on $G$ we show that the Beurling algebra $L^1(G, \omega)$ is weakly amenable if and only if there is no nontrivial continuous group homomorphism $\phi$: $G\to \mathbb{C}$ such that $\sup_{t\in G}\frac{|\phi(t)|}{\omega(t)\omega(t^{-1})} < \infty$. Let $\hat\omega(t) = \limsup_{s\to \infty}\omega(ts)/\omega(s)$ ($t\in G$). Then $L^1(G, \omega)$ is 2-weakly amenable if there is a constant $m> 0$ such that $\liminf_{n\to \infty}\frac{\omega(t^n)\hat\omega(t^{-n})}{n} \leq m$ for all $t\in G$. Comment: To appear in Proc. Amer. Math. Soc |
| Databáze: | arXiv |
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