亚正则算子的结构性质与正常性准则
Structural Properties and Normality Criteria for Subclasses of Normaloid Operators
AI总结：
本文研究了亚正则算子的结构性质与正常性准则，通过绝对-(p,r)-准正常性和紧算子的条件，证明了算子的正常性及紧正常性。
摘要：
我们研究了某些有界线性算子在希尔伯特空间上的结构性质和正常性准则。我们证明，一个具有极分解T=U|T|的算子T是自伴的，当且仅当T是绝对-(p,r)-准正常且部分等距U是自伴的。扩展安多定理，我们证明，如果T是绝对-(p,r)-准正常且T^n是正常算子（n∈N），则T本身是正常算子。我们进一步证明，如果T是绝对-(p,r)-准正常且T²是紧算子，则T是紧正常算子。最后，我们获得了在正常oid层级内准正常部分等距的若干特征化结果。
英文摘要：
We investigate structural properties and normality criteria for certain classes of bounded linear operators on a Hilbert space. We show that an operator $T$ with polar decomposition $T = U|T|$ is self-adjoint if and only if $T$ is absolute-$(p,r)$-paranormal and the partial isometry $U$ is self-adjoint. Extending Ando's Theorem, we prove that if $T$ is absolute-$(p,r)$-paranormal and $T^n$ is normal for some $n \in \mathbb{N}$, then $T$ itself is normal. We further show that if $T$ is absolute-$(p,r)$-paranormal and $T^2$ is compact, then $T$ is a compact normal operator. Finally, we obtain several characterizations of quasinormal partial isometries within the normaloid hierarchy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
