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Weighted composition operators on extended analytic Lipschitz algebras | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 04 آبان 1403 اصل مقاله (417.09 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 | ||
| تاریخ دریافت: 29 آذر 1402، تاریخ پذیرش: 13 بهمن 1402 | ||
| 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 | ||
| مراجع | ||
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