论文标题
阴影，广义双曲线和Aluthge变换
Shadowing, Generalized hyperbolic and Aluthge transforms
论文作者
论文摘要
在本说明中，我们介绍了$ r $ homoclinic点的概念。我们表明，当且仅当它在阴影下并且没有非零$ r $ r $ homoclinic点时，Banach空间上的操作员才是双曲线。我们还解决了Banach空间上的阴影操作员的不变子空间问题（ISP）。之后，我们验证一组广义双曲线操作员在$λ$ -Arthge下对每个$λ\ in \ left（0,1 \ right）$不变。接下来，仅当初始操作员是双曲线时，Aluthge迭代可逆操作员会收敛到双曲线操作员。最后，我们证明了偏移双曲双侧加权移动的迭代率有分歧，并且双曲双侧加权转移随着发散的Aluthge Itererates存在。
In this note, we introduce the notion of $r$-homoclinic points. We show that an operator on a Banach space is hyperbolic if and only if it is shadowing and has no nonzero $r$-homoclinic points. We also solve invariant subspace problem (ISP for brevity) for shadowing operators on Banach spaces. Afterwards, we verify that the set of generalized hyperbolic operators is invariant under $λ$-Aluthge transforms for every $λ\in \left( 0,1 \right)$. Next, the Aluthge iterates of invertible operators converge to hyperbolic operators only if the initial operators are hyperbolic. Finally, we prove that the Aluthge iterates of shifted hyperbolic bilateral weighted shifts diverge and that hyperbolic bilateral weighted shifts with divergent Aluthge iterates exist.
