论文标题
从线性动力学的角度来研究主教操作员
A study of Bishop operators from the point of view of linear dynamics
论文作者
论文摘要
在本文中，我们从$ l ^ p（[0，1]）$上研究所谓的主教操作员$ t_α$，从线性动力学的角度来看，$α\ in（0，1）$和$ 1 <p < + \ infty $。我们表明它们从来都不是超环或超级环节，并研究了这些结果的扩展为加权翻译操作员的情况。然后，我们研究主教操作员的循环性$ t_α$。基于Chalendar和Partington的结果，在$α$合理的情况下，我们表明$ t_α$对于密集的$ g_δ$ - 非理性$α$的密集$ g_δ$ set，讨论环状功能，并提供$α\ in \ mathbf r \ r \ backslash sy cy cy的条件。
In this paper, we study the so-called Bishop operators $T _ α$ on $L ^ p ([0, 1])$, with $α\in (0, 1)$ and $1 < p < + \infty$, from the point of view of linear dynamics. We show that they are never hypercyclic nor supercyclic, and investigate extensions of these results to the case of weighted translation operators. We then investigate the cyclicity of the Bishop operators $T _ α$. Building on results by Chalendar and Partington in the case where $α$ is rational, we show that $T _ α$ is cyclic for a dense $G _ δ$-set of irrational $α$'s, discuss cyclic functions and provide conditions in terms of convergents of $α\in \mathbf R \backslash \mathbf Q$ implying that certain functions are cyclic.
