论文标题
c_ {1。}类弱的超级环保界限运算符
Weakly Supercyclic Power Bounded Operators of Class C_{1.}
论文作者
论文摘要
$ c_ {1 {\ textstyle \ cdot}}} $没有超级环保的限制性操作员。但是，存在微弱的l-依次的超级级别的单一操作员$。$。 $ \ widehat t $，是一个弱的l-序列的超级环境奇异连续统一（并且，每当$ t $ ne $ t $ sever stable）$。上述结果暗示$σ_ {\ kern-1ptp}（t）=σ_ {\ kern-1ptp}（t^*）= \ varnothing $，并且如果一个弱的l- sequercyclyclyclyclyclicclic oterator与等轴测器相似，则它与单位运算符相似。
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 $σ_{\kern-1ptP}(T)=σ_{\kern-1ptP}(T^*)=\varnothing$, and also that if a weakly l-sequentially supercyclic operator is similar to an isometry, then it is similar to a unitary operator.
