Geodesic
Maximal distributional chaos of weighted shift operators on Köthe sequence spaces
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 105-114 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $0 \epsilon \mathop{\rm diam} \lambda _{p}(A)$.
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 $0 \epsilon \mathop{\rm diam} \lambda _{p}(A)$.
DOI : 10.1007/s10587-014-0087-8
Classification : 26A18, 28D20, 37B40, 37D45, 54H20
Keywords: weighted shift operator; principal measure; distributional chaos 
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Wu, Xinxing. Maximal distributional chaos of weighted shift operators on Köthe sequence spaces. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 105-114. doi: 10.1007/s10587-014-0087-8

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