Weakly compact weighted composition operators on pointed Lipschitz spaces
Author(s):
Article Type:
Research/Original Article (بدون رتبه معتبر)
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 $x \in X \backslash \{x_{0}\}.$
Keywords:
Language:
English
Published:
Caspian Journal of Mathematical Sciences, Volume:13 Issue: 1, Winter Spring 2024
Pages:
49 to 61
https://www.magiran.com/p2755818
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