与Volterra算子交换的算子不是弱超循环的
Operators commuting with the Volterra operator are not weakly supercyclic
摘要：
本文证明了$L_p[0,1]$上的任何有界线性算子（对于$1\leq p<\infty$）与Volterra算子$V$交换时，都不是弱超循环的，从而肯定地回答了Léon-Saavedra和Piqueras-Lerena提出的一个问题.它是通过提供一个代数风味的条件，防止它是弱超循环的运营商，并满足任何运营商与$V$交换。
英文摘要：
We prove that any bounded linear operator on $L_p[0,1]$ for $1\leq p<\infty$, commuting with the Volterra operator $V$, is not weakly supercyclic, which answers affirmatively a question raised by Léon-Saavedra and Piqueras-Lerena. It is achieved by providing an algebraic flavored condition on an operator which prevents it from being weakly supercyclic and is satisfied for any operator commuting with $V$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
