Department of Mathematics, Faculty of Science, Arak University
10.22080/cjms.2023.26011.1668
Abstract
Let $(X,d)$ be a pointed compact metric space with the base point $x_{0}$ and let $\Lip((X,d),x_{0})$ $(\lip((X,d),x_{0}))$ denote the pointed (little) Lipschitz space on $(X,d)$. In this paper, we prove that every weakly compact composition operator $u C_{\varphi}$ on $\Lip((X,d), x_{0})$ is compact provided that $\lip((X,d),x_{0})$ has the uniform separation property, ${\varphi}$ is a base point preserving Lipschitz self-map of $X$ and $u \in \Lip(X,d)$ with $u(x) \neq0$ for all $x \in X \backslash \{x_{0}\}.$
Barzegari, R., Alimohammadi, D. (2024). 'Weakly compact weighted composition operators on pointed Lipschitz spaces', Caspian Journal of Mathematical Sciences (CJMS), 13(1), pp. 49-61. doi: 10.22080/cjms.2023.26011.1668
VANCOUVER
Barzegari, R., Alimohammadi, D. Weakly compact weighted composition operators on pointed Lipschitz spaces. Caspian Journal of Mathematical Sciences (CJMS), 2024; 13(1): 49-61. doi: 10.22080/cjms.2023.26011.1668
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