$n$-weak amenability of a certain class of function spaces

Document Type : Research Paper


Faculty of Mathematical Sciences, Shahrood University of Technology, P. O. Box 3619995161-316, Shahrood, Iran.



Let $A$ be a non-zero normed vector space and let $\varphi$ be a non-zero element of $A^*$ such that $\Vert \varphi \Vert \leq 1$. Assume that $K=\overline{B_1^{(0)}}$ is the closed unit ball of $A$. According to the our recent studies on the spaces of $(C^{b\varphi}(K), \Vert \cdot \Vert_\infty)$ and $(C^{b\varphi}(K), \Vert \cdot \Vert_\varphi)$, generated by $C^b(K)$ and equipped with a new product `` $ \cdot $ '' and different norms $\Vert \cdot \Vert_\infty $ and $\Vert \cdot \Vert_\varphi$, the $n-$weak amenability of $(C^{b\varphi}(K), \Vert \cdot \Vert_\infty)$ and $(C^{b\varphi}(K), \Vert \cdot \Vert_\varphi)$ are investigated. 


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