AI 中文总结
该研究推广Bernardes等人的定理，刻画巴拿赫序列空间加权移位及连续函数空间加权复合算子的伪轨跟踪性质，给出相关算子具有该性质的充分条件及乘法算子的完整刻画。
AI 中文摘要
本工作刻画了一类一般巴拿赫序列空间上加权移位的伪轨跟踪性质，推广了Bernardes等人在ETDS（2020）中证明的定理。随后将该结果应用于刻画作用于一类连续函数巴拿赫空间上加权复合算子的伪轨跟踪性质。作为应用，给出了$C_b(\boldsymbol{R})$和$C_0(\boldsymbol{R})$空间上双边加权平移的伪轨跟踪性质刻画。在更一般的框架下，提供了加权复合算子具有伪轨跟踪性质的充分条件，这些条件可用于得到Hardy空间$H^p(\boldsymbol{D})$（$p\in[1,\infty]$）、$H^\infty(\Omega)$型空间及$C_b(\Theta)$空间上乘法算子的该性质的完整刻画。
英文摘要
In this work, we characterize the shadowing property for weighted shifts on a general class of Banach sequence spaces, extending a theorem proved by Bernardes et al. in ETDS (2020). We then apply this result to characterize this property for weighted composition operators acting on a class of Banach spaces of continuous functions. As an application, we present a characterization of shadowing for bilateral weighted translations on the spaces $C_b(\mathbb{R})$ and $C_0(\mathbb{R})$. In a more general setting, we provide sufficient conditions for weighted composition operators to have the shadowing property. These conditions allow us to obtain complete characterizations of this property for multiplication operators on the Hardy spaces $H^p(\mathbb{D})$, $p\in[1,\infty]$, as well as on spaces of the form $H^\infty(Ω)$ or $C_b(Θ)$.
Comments27 pages
