MEAN SENSITIVITY AND BANACH MEAN SENSITIVITY FOR LINEAR OPERATORS

doi:10.1007/s10473-024-0402-x

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (4): 1200-1228.doi: 10.1007/s10473-024-0402-x

MEAN SENSITIVITY AND BANACH MEAN SENSITIVITY FOR LINEAR OPERATORS

Quanquan Yao^*, Peiyong Zhu

School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China

收稿日期:2022-07-22 修回日期:2022-10-27 出版日期:2024-08-25 发布日期:2024-08-30

MEAN SENSITIVITY AND BANACH MEAN SENSITIVITY FOR LINEAR OPERATORS

Quanquan Yao^*, Peiyong Zhu

School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China

Received:2022-07-22 Revised:2022-10-27 Online:2024-08-25 Published:2024-08-30
Contact: *E-mail: yqqmath@163.com
About author:E-mail: zpy6940@sina.com.cn
Supported by:
This work was supported by the NSFC (11501391).

摘要/Abstract

摘要： Let $(X,T)$ be a linear dynamical system, where $X$ is a Banach space and $T:X \to X$ is a bounded linear operator. This paper obtains that $(X,T)$ is sensitive (Li-Yorke sensitive, mean sensitive, syndetically mean sensitive, respectively) if and only if $(X,T)$ is Banach mean sensitive (Banach mean Li-Yorke sensitive, thickly multi-mean sensitive, thickly syndetically mean sensitive, respectively). Several examples are provided to distinguish between different notions of mean sensitivity, syndetic mean sensitivity and mean Li-Yorke sensitivity.

关键词: mean sensitive, Banach mean sensitive, syndetically mean sensitive, Li-Yorke sensitive, mean Li-Yorke sensitive

Abstract: Let $(X,T)$ be a linear dynamical system, where $X$ is a Banach space and $T:X \to X$ is a bounded linear operator. This paper obtains that $(X,T)$ is sensitive (Li-Yorke sensitive, mean sensitive, syndetically mean sensitive, respectively) if and only if $(X,T)$ is Banach mean sensitive (Banach mean Li-Yorke sensitive, thickly multi-mean sensitive, thickly syndetically mean sensitive, respectively). Several examples are provided to distinguish between different notions of mean sensitivity, syndetic mean sensitivity and mean Li-Yorke sensitivity.

Key words: mean sensitive, Banach mean sensitive, syndetically mean sensitive, Li-Yorke sensitive, mean Li-Yorke sensitive

中图分类号:

47A16

Quanquan Yao, Peiyong Zhu. MEAN SENSITIVITY AND BANACH MEAN SENSITIVITY FOR LINEAR OPERATORS[J]. 数学物理学报(英文版), 2024, 44(4): 1200-1228.

Quanquan Yao, Peiyong Zhu. MEAN SENSITIVITY AND BANACH MEAN SENSITIVITY FOR LINEAR OPERATORS[J]. Acta mathematica scientia,Series B, 2024, 44(4): 1200-1228.

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MEAN SENSITIVITY AND BANACH MEAN SENSITIVITY FOR LINEAR OPERATORS

MEAN SENSITIVITY AND BANACH MEAN SENSITIVITY FOR LINEAR OPERATORS

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