Weighted composition operators on extended analytic Lipschitz algebras

	Weighted composition operators on extended analytic Lipschitz algebras
International Journal of Nonlinear Analysis and Applications
مقاله 11، دوره 16، شماره 8، آبان 2025، صفحه 121-134 اصل مقاله (417.28 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.32727.4871
نویسندگان
Rezvan Barzegari؛ Davood Alimohammadi^*
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
چکیده
In this paper, we study weighted composition operators on extended analytic Lipschitz algebras ${\rm Lip}_{A}(X,K,\alpha)$ where $X$ is a compact plane set, $K$ is a closed subset of $X$ with nonempty interior and $0 < \alpha \leq 1$. We first give necessary conditions and sufficient conditions on a function $u \in \mathbb{C} ^{X}$ and self-map $\varphi$ of $X$ for which $T=uc_{\varphi}$ to be a weighted composition operator on ${\rm Lip}_{A}(X,K,\alpha)$. We next give the necessary conditions for these operators to be compact and provide some sufficient conditions for the compactness of such operators.
کلیدواژه‌ها
Extended analytic Lipschitz algebra‎؛ ‎Analytic uniform algebra‎؛ ‎Banach function algebra‎؛ ‎Compact operator‎؛ ‎Composition operator‎؛ ‎Weighted composition operator
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