论文标题
$ l^p $空间上的构图运营商的扩展性和强大的结构稳定性
Expansivity and strong structural stability for composition operators on $L^p$ spaces
论文作者
论文摘要
在本说明中，我们调查了$ l^p $空间上的构图运营商的膨胀性和强大结构稳定性的概念，$ 1 \ leq p <\ infty $。在一般情况和耗散案例中，都提供了为该操作员提供膨胀的必要条件和足够的条件。我们还表明，在耗散的环境中，阴影特性意味着强大的结构稳定性，我们证明这两个概念在积极扩张的额外假设下是等效的。
In this note we investigate the two notions of expansivity and strong structural stability for composition operators on $L^p$ spaces, $1 \leq p < \infty$. Necessary and sufficient conditions for such operators to be expansive are provided, both in the general and the dissipative case. We also show that, in the dissipative setting, the shadowing property implies the strong structural stability and we prove that these two notions are equivalent under the extra hypothesis of positive expansivity.
