关于非经典数列空间及其以外的超循环性和线性混沌
On hypercyclicity and linear chaos in a nonclassical sequence space and beyond
摘要：
我们分析了超循环性，混沌性和谱结构（有界和无界）加权后向移位在非经典数列空间，空间$l_1$的可和序列都是等距同构，连续和密集嵌入。基于加权后移，我们进一步构造了非经典数列空间和经典空间$l_1$中新的有界和无界线性超循环和混沌算子，包括那些超循环但非混沌的算子.
英文摘要：
We analyze the hypercyclicity, chaoticity, and spectral structure of (bounded and unbounded) weighted backward shifts in a nonclassical sequence space, which the space $l_1$ of summable sequences is both isometrically isomorphic to and continuously and densely embedded into. Based on the weighted backward shifts, we further construct new bounded and unbounded linear hypercyclic and chaotic operators both in the nonclassical sequence space and the classical space $l_1$, including those that are hypercyclic but not chaotic.
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