A Note on the Spectrum of Some Composition Operators on Korenblum Type Spaces

被引：0
作者：
Pablo Galindo
Esther Gómez-Orts
机构：
[1] Universidad de Valencia,Departamento de Análisis Matemático
[2] Instituto Universitario de Matemática Pura y Aplicada IUMPA. Universidad Politécnica de Valencia,undefined
来源：
Results in Mathematics | 2021年 / 76卷
关键词：
Composition operator; spectrum; analytic functions; growth Banach spaces; Korenblum space; Fréchet spaces; (LB)-spaces; 47B33; 46E10;
D O I：
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摘要：
We prove that under some mild conditions on the symbol φ,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi ,$$\end{document} the spectrum of the corresponding composition operator Cφ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_\varphi $$\end{document} on the Korenblum type spaces A--α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_{-}^{-\alpha }$$\end{document} and A+-α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_{+}^{-\alpha }$$\end{document} contains a closed ball of positive radius.
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