Let $(X,d)$ be a compact metric 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 $$p_{(K,d^\alpha)}(f)=\sup\{\frac{|f(x)-f(y)|}{d^\alpha(x,y)} : x,y\in K , x\neq y\}<\infty$$ when it is equipped with the algebra norm $||f||_{{\rm Lip}(X, K, d^ {\alpha})}= ||f||_X+ p_{(K,d^{\alpha})}(f)$, where $||f||_X=\sup\{|f(x)|:~x\in X \}$. In this paper we first study the structure of certain ideals of ${\rm Lip}(X,K,d^\alpha)$. Next we show that if $K$ is infinite and ${\rm int}(K)$ contains a limit point of $K$ then ${\rm Lip}(X,K,d^\alpha)$ has at least a nonzero continuous point derivation and applying this fact we prove that ${\rm Lip}(X,K,d^\alpha)$ is not weakly amenable and amenable.
Mayghani, M., Alimohammadi, D. (2017). The structure of ideals, point derivations, amenability and weak amenability of extended Lipschitz algebras. International Journal of Nonlinear Analysis and Applications, 8(1), 389-404. doi: 10.22075/ijnaa.2016.493
MLA
Maliheh Mayghani; Davood Alimohammadi. "The structure of ideals, point derivations, amenability and weak amenability of extended Lipschitz algebras". International Journal of Nonlinear Analysis and Applications, 8, 1, 2017, 389-404. doi: 10.22075/ijnaa.2016.493
HARVARD
Mayghani, M., Alimohammadi, D. (2017). 'The structure of ideals, point derivations, amenability and weak amenability of extended Lipschitz algebras', International Journal of Nonlinear Analysis and Applications, 8(1), pp. 389-404. doi: 10.22075/ijnaa.2016.493
VANCOUVER
Mayghani, M., Alimohammadi, D. The structure of ideals, point derivations, amenability and weak amenability of extended Lipschitz algebras. International Journal of Nonlinear Analysis and Applications, 2017; 8(1): 389-404. doi: 10.22075/ijnaa.2016.493
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