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arXiv 2004.05253math.FA
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C_{1.}类的弱超循环幂有界算子

Weakly Supercyclic Power Bounded Operators of Class C_{1.}

C. S. Kubrusly, B. P. Duggal

发表信息：
Adv. Math. Sci. Appl. 30 (2021), no.2, 571-585
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摘要：

不存在$C_{1{\textstyle\cdot}}.$类的超循环幂有界算子，但存在弱l-序列超循环酉算子$.$.本文证明了：如果$T$是$C_{1{\textstyle\cdot}}$类的弱l-序列超循环幂有界算子，则它有扩张$\widehat T$是弱l-序列超循环奇异连续酉（并且只要$T$是弱稳定的，$\widehat T$就具有Rajchman标量谱测度）$.$上述结果意味着$σ_{\kern-1ptP}(T)=σ_{\kern-1ptP}(T^*)=\varnothing$，并且如果弱l-序列超循环算子类似于等距，则它类似于酉算子。

英文摘要：

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.

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