Weakly compact weighted composition operators on pointed Lipschitz spaces

Message:
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 $x \in X \backslash \{x_{0}\}.‎‎‎‎$
Language:
English
Published:
Caspian Journal of Mathematical Sciences, Volume:13 Issue: 1, Winter Spring 2024
Pages:
49 to 61
https://www.magiran.com/p2755818  
سامانه نویسندگان
  • Corresponding Author (2)
    Davood Alimohammadi
    Associate Professor Department of Mathematics, Faculty of Science, Arak University, University Of Arak, Arak, Iran
    Alimohammadi، Davood
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