@article {
author = {Mayghani, Maliheh and Alimohammadi, Davood},
title = {The structure of ideals, point derivations, amenability and weak amenability of extended Lipschitz algebras},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {8},
number = {1},
pages = {389-404},
year = {2017},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2016.493},
abstract = {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$$p_{(K,d^\alpha)}(f)=\sup\{\frac{|f(x)-f(y)|}{d^\alpha(x,y)} : x,y\in K , x\neq y\}<\infty$$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.},
keywords = {Amenability,Banach function algebra,extended Lipschitz algebra,point derivation,weak amenability},
url = {https://ijnaa.semnan.ac.ir/article_493.html},
eprint = {https://ijnaa.semnan.ac.ir/article_493_c33ba9a36bbd03e49c6d1e1671e3f46e.pdf}
}