发表机构
Gandhi Institute of Technology and Management (Deemed to be University); Siksha ‘O’ Anusandhan (Deemed to be University)（甘地理工学院（认定为大学）; 锡卡奥阿努桑丹（认定为大学））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究线性算子的渐近扩张性，引入强与超渐近扩张概念，证明有限维下等价于双曲性，无限维下超渐近扩张等价于双曲性，且其在强算子拓扑中稠密。
AI 中文摘要
我们研究了线性算子的拓扑动力学概念——渐近扩张性。我们还引入了两个新概念，即强渐近扩张性和超渐近扩张性。我们证明了在有限维空间上，这三个概念都等价于双曲性。在无限维情形下，我们构造了例子来说明渐近扩张性弱于强渐近扩张性，而强渐近扩张性又弱于超渐近扩张性。更有趣的是，我们证明了超渐近扩张性等价于双曲性概念。然后，我们证明了超渐近扩张线性算子在强算子拓扑中是一个稠密类。最后，我们展示了构造渐近扩张线性算子变体的优雅方法。
英文摘要
We study the topological dynamical notion of asymptotic expansivity for linear operators. We also introduce two new notions, namely strong asymptotic expansivity and super asymptotic expansivity. We show that all three notions are equivalent to hyperbolicity for linear operators on finite dimensional spaces. In case of infinite-dimension, we construct examples to show that asymptotic expansivity is weaker than strong asymptotic expansivity which is further weaker than super asymptotic expansivity. More interestingly, we prove that super asymptotic expansivity is equivalent to the notion of hyperbolicity. Then, we prove that the super asymptotically expansive linear operators is a dense class in strong operator topology. Finally, we show elegant ways to construct variants of asymptotically expansive linear operators.
Comments25 pages
