论文标题
多项式紧凑型运算符集的HyperVariant子空间
Hyperinvariant subspaces for sets of polynomially compact operators
论文作者
论文摘要
我们证明了几组多项式紧凑型运算符的非平凡性高渗水子空间的存在。本文的主要结果是： （i）一个非平凡的规范封闭代数$ \ Mathcal A \ subseteq \ Mathcal B（\ Mathscr X）$，由多项式紧凑的quasinilpotent运算符组成，具有非平凡的HyperInvariant子空间； （ii）如果存在由操作员频段$ \ Mathcal S $生成的代数的规范闭合中的非零紧凑型操作员，则$ \ Mathcal S $具有非平凡的HyperVariant子空间。
We prove the existence of a non-trivial hyperinvariant subspace for several sets of polynomially compact operators. The main results of the paper are: (i) a non-trivial norm closed algebra $\mathcal A\subseteq \mathcal B(\mathscr X)$ which consists of polynomially compact quasinilpotent operators has a non-trivial hyperinvariant subspace; (ii) if there exists a non-zero compact operator in the norm closure of the algebra generated by an operator band $\mathcal S$, then $\mathcal S$ has a non-trivial hyperinvariant subspace.
