论文标题
在收敛序列的线性混乱上
On linear chaos in the space of convergent sequences
论文作者
论文摘要
我们表明，无法通过仅扩展空间中的加权向后移动$ C_0（\ Mathbb {n}）$的变化序列，无法达到收敛序列的空间中的线性混乱。为了应用新发现的线性混乱条件，我们提供了简洁的证据证明了上述操作员的混乱性及其力量，并列出了它们的光谱结构。我们在$ c（\ mathbb {n}）$中进一步构建了与$ C_0（\ Mathbb {Z} _+）$在两个空间之间的同构同构中以$ c（\ mathbb {z} _+）$相连的构造和无限的线性混沌操作员。
We show that linear chaos in the space $c(\mathbb{N})$ of convergent sequences cannot be arrived at by merely extending the weighted backward shifts in the space $c_0(\mathbb{N})$ of vanishing sequences. Applying a newly found sufficient condition for linear chaos, we furnish concise proofs of the chaoticity of the foregoing operators along with their powers and also itemize their spectral structure. We further construct bounded and unbounded linear chaotic operators in $c(\mathbb{N})$ as conjugate to the chaotic backward shifts in $c_0(\mathbb{Z}_+)$ via a homeomorphic isomorphism between the two spaces.
