幂类似于次正规算子的算子

Pub Date : 2015-07-01 DOI:10.18910/57659

Sungeun Jung, E. Ko, Mee-Jung Lee

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引用次数: 1

摘要

本文研究了算子的幂相似度。特别地，我们证明了如果$T \ In \mathit{PS}(H)$(定义见下)对于一些次正规算子$H$，则$T$是子标量。由此得到了这样一个富谱算子具有非平凡不变子空间。此外，我们考虑$T \in \mathit{PS}(H)$的不变子空间和超不变子空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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ON OPERATORS WHICH ARE POWER SIMILAR TO HYPONORMAL OPERATORS

In this paper, we study power similarity of operators. In particular, we show that if $T \in \mathit{PS}(H)$ (defined below) for some hyponormal operator $H$, then $T$ is subscalar. From this result, we obtain that such an operator with rich spectrum has a nontrivial invariant subspace. Moreover, we consider invariant and hyperinvariant subspaces for $T \in \mathit{PS}(H)$.

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