Mean ergodicity of composition operators on Hardy space

被引：0

作者：

Shi-An Han

Ze-Hua Zhou

机构：

[1] Civil Aviation University of China,College of Science

[2] Tianjin University,School of Mathematics

来源：

Proceedings - Mathematical Sciences | 2019年 / 129卷

关键词：

Composition operator; mean ergodic; Hardy space; 47B33; 47B38;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this article, we investigate the mean ergodicity of composition operators acting on the Hardy space Hp(D)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^p({\mathbb {D}})$$\end{document}, 1≤p<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\le p<\infty $$\end{document}. Specifically, a 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} acting on Hp(D)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^p({\mathbb {D}})$$\end{document} is mean ergodic if and only if 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} has an interior fixed point, in which case 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} is uniformly mean ergodic if and only if 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} is an elliptic automorphism of finite order or a non-automorphism that is not inner.

引用

共 27 条

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