Maximal distributional chaos of weighted shift operators on Köthe sequence spaces

Title:

Maximal distributional chaos of weighted shift operators on Köthe sequence spaces

Creator:

Wu, Xinxing

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:71e87c3e-819d-41f8-b74a-9315421036b8
uuid:71e87c3e-819d-41f8-b74a-9315421036b8

Subject:

weighted shift operator, principal measure, and distributional chaos

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

During the last ten some years, many research works were devoted to the chaotic behavior of the weighted shift operator on the Köthe sequence space. In this note, a sufficient condition ensuring that the weighted shift operator $B_{w}^{n}\colon \lambda _{p}(A)\to \lambda _{p}(A)$ defined on the Köthe sequence space $\lambda _{p}(A)$ exhibits distributional $\epsilon $-chaos for any $0< \epsilon < \mathop{\rm diam} \lambda _{p}(A)$ and any $n\in \mathbb {N}$ is obtained. Under this assumption, the principal measure of $B_{w}^{n}$ is equal to 1. In particular, every Devaney chaotic shift operator exhibits distributional $\epsilon $-chaos for any $0< \epsilon < \mathop{\rm diam} \lambda _{p}(A)$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

105-114

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:1

Harvested from:

CDK

Metadata only:

false