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A note on supercyclic vectors of Hilbert space operators
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-07-14 , DOI: 10.1016/j.jmaa.2021.125500
Masoumeh Faghih-Ahmadi 1 , Karim Hedayatian 1
Affiliation  

Let H be an infinite dimensional complex Hilbert space and T be a bounded linear operator on H. We show that if there exists xH such that the closure of {αTnx:αC,n0} is H, then there is a subsequence (nk)k=1 such that the closed linear span of {Tnkx:k1} is not the whole space H.



中文翻译:

关于 Hilbert 空间算子的超循环向量的注记

H是一个无限维复数希尔伯特空间,TH上的一个有界线性算子。我们证明如果存在XH 使得关闭 {αnXαC,n0}H,则有子序列(n)=1 使得闭合线性跨度 {nX1}不是整个空间H

更新日期:2021-07-22
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