| Autor: |
Kubrusly, C. S., Duggal, B. P. |
| Rok vydání: |
2020 |
| Předmět: |
|
| Zdroj: |
Adv. Math. Sci. Appl. 30 (2021), no.2, 571-585 |
| Druh dokumentu: |
Working Paper |
| Popis: |
There is no supercyclic power bounded operator of class $C_{1{\textstyle\cdot}}.$ There exist, however, weakly l-sequentially supercyclic unitary operators$.$ We show that if $T$ is a weakly l-sequentially supercyclic power bounded operator of class $C_{1{\textstyle\cdot}}$, then it has an extension $\widehat T$ which is a weakly l-sequentially supercyclic singular-continuous unitary (and $\widehat T$ has a Rajchman scalar spectral measure whenever $T$ is weakly stable)$.$ The above result implies $\sigma_{\kern-1ptP}(T)=\sigma_{\kern-1ptP}(T^*)=\varnothing$, and also that if a weakly l-sequentially supercyclic operator is similar to an isometry, then it is similar to a unitary operator. |
| Databáze: |
arXiv |
| Externí odkaz: |
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