| Title:
|
Maximal distributional chaos of weighted shift operators on Köthe sequence spaces (English) |
| Author:
|
Wu, Xinxing |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
105-114 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $0< \epsilon < \mathop{\rm diam} \lambda _{p}(A)$. (English) |
| Keyword:
|
weighted shift operator |
| Keyword:
|
principal measure |
| Keyword:
|
distributional chaos |
| MSC:
|
26A18 |
| MSC:
|
28D20 |
| MSC:
|
37B40 |
| MSC:
|
37D45 |
| MSC:
|
54H20 |
| idZBL:
|
Zbl 06391480 |
| idMR:
|
MR3247448 |
| DOI:
|
10.1007/s10587-014-0087-8 |
| . |
| Date available:
|
2014-09-29T09:39:22Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143953 |
| . |
| Reference:
|
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