On the continuous Cesàro operator in certain function spaces

被引:0
作者
Angela A. Albanese
José Bonet
Werner J. Ricker
机构
[1] Università del Salento,Dipartimento di Matematica e Fisica “E. De Giorgi”
[2] Universitat Politécnica de Valéncia,Instituto Universitario de Matemática Pura y Aplicada IUMPA
[3] Katholische Universität Eichstätt-Ingolstadt,Math.
来源
Positivity | 2015年 / 19卷
关键词
Cesàro operator; Continuous function spaces; -spaces; (Uniformly) mean ergodic operator; Hypercyclic operator; Supercyclic operator; Primary 47A10; 47A16; 47A35; Secondary 46A04; 47B34; 47B38;
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摘要
Various properties of the (continuous) Cesàro operator C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {C}$$\end{document}, acting on Banach and Fréchet spaces of continuous functions and Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-spaces, are investigated. For instance, the spectrum and point spectrum of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {C}$$\end{document} are completely determined and a study of certain dynamics of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {C}$$\end{document} is undertaken (eg. hyper- and supercyclicity, chaotic behaviour). In addition, the mean (and uniform mean) ergodic nature of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {C}$$\end{document} acting in the various spaces is identified.
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页码:659 / 679
页数:20
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