AI 中文总结
本文研究有限维巴拿赫空间、希尔伯特空间上线性算子的拓扑跟踪性，明确其谱的范围条件，得出相关算子的非游荡点性质。
AI 中文摘要
我们证明：有限维巴拿赫空间上的线性算子具有文献[lny]中引入的拓扑跟踪性，当且仅当其谱位于开复单位圆盘内或该圆盘的闭包之外。此外，每个具有拓扑跟踪性的一致膨胀线性算子的谱也位于开复单位圆盘内或该圆盘的闭包之外。最后，我们证明希尔伯特空间上具有拓扑跟踪性的正规算子不存在任何非零非游荡点。
英文摘要
We prove a linear operator of a finite-dimensional Banach space has the topological shadowing property, as introduced in \cite{lny}, if and only if its spectrum lies either within the open unit complex disk or outside the closure of that disk. Moreover, the spectrum of every uniformly expansive linear operator with the topological shadowing property lies either within the open unit complex disk or outside the closure of that disk. Lastly, we prove that a normal operator with the topological shadowing property on a Hilbert space does not have any nonzero nonwandering points.
Comments12 pages
