Geodesic
Maximal distributional chaos of weighted shift operators on Köthe sequence spaces
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 105-114.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{10_1007_s10587_014_0087_8,
     author = {Wu, Xinxing},
     title = {Maximal distributional chaos of weighted shift operators on {K\"othe} sequence spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {105--114},
     publisher = {mathdoc},
     volume = {64},
     number = {1},
     year = {2014},
     doi = {10.1007/s10587-014-0087-8},
     mrnumber = {3247448},
     zbl = {06391480},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0087-8/}
}
TY  - JOUR
AU  - Wu, Xinxing
TI  - Maximal distributional chaos of weighted shift operators on Köthe sequence spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2014
SP  - 105
EP  - 114
VL  - 64
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0087-8/
DO  - 10.1007/s10587-014-0087-8
LA  - en
ID  - 10_1007_s10587_014_0087_8
ER  - 
%0 Journal Article
%A Wu, Xinxing
%T Maximal distributional chaos of weighted shift operators on Köthe sequence spaces
%J Czechoslovak Mathematical Journal
%D 2014
%P 105-114
%V 64
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0087-8/
%R 10.1007/s10587-014-0087-8
%G en
%F 10_1007_s10587_014_0087_8
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. http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0087-8/

Cité par Sources :