论文标题
希尔伯特太空运营商的新订单
New Orders Among Hilbert Space Operators
论文作者
论文摘要
本文介绍了相关的希尔伯特太空运营商之间的几个新关系。特别是，我们证明了$ t，| t |，\ mathcal {r} t，\ mathcal {i} t，| t | t |+| t^*| $和许多其他相关形式，作为该领域的新讨论；其中$ \ mathcal {r} t $和$ \ Mathcal {i} t $是操作员$ t $的真实和虚构部分。我们的方法将基于证明某些新矩阵操作员的积极性，在该矩阵运算符中，将以积极矩阵运算符的几种新形式作为获得其他排序结果的关键工具。作为应用程序，我们提出了一些结果，该结果以某种方式将一些已知结果扩展到这个方向的方式处理数值半径不平等，此外还有一些有关奇异值的结果。
This article introduces several new relations among related Hilbert space operators. In particular, we prove some Löewner partial orderings among $T, |T|, \mathcal{R}T, \mathcal{I}T, |T|+|T^*|$ and many other related forms, as a new discussion in this field; where $\mathcal{R}T$ and $\mathcal{I}T$ are the real and imaginary parts of the operator $T$. Our approach will be based on proving the positivity of some new matrix operators, where several new forms for positive matrix operators will be presented as a key tool in obtaining the other ordering results. As an application, we present some results treating numerical radius inequalities in a way that extends some known results in this direction, in addition to some results about the singular values.
