论文标题
$ a $ numerical半径正交性和半希尔伯特太空运营商的并行性及其应用
$A$-Numerical radius orthogonality and parallelism of semi-Hilbertian space operators and their applications
论文作者
论文摘要
在本文中，我们旨在介绍和表征运算符数字半径正交性在复杂的Hilbert Space $ \ Mathcal {H} $上的概念，该{H} $与$ \ \ nathcal {h} $ a $ a $ a $ a $ a $ a $ a $ a $ augion的半音符有限。此外，证明了$ a-numerical radius Parallelelism $ a-lank的表征。作为获得的结果的应用，我们获得了一些$ \ mathbb {a} $ - 运算符矩阵的数值半径不平等，其中$ \ mathbb {a} $是具有对角线条目的操作员对角线矩阵，是正面操作员$ a $。还研究了其他一些相关结果。
In this paper, we aim to introduce and characterize the concept of numerical radius orthogonality of operators on a complex Hilbert space $\mathcal{H}$ which are bounded with respect to the semi-norm induced by a positive operator $A$ on $\mathcal{H}$. Moreover, a characterization of the $A$-numerical radius parallelism for $A$-rank one operators is proved. As applications of the obtained results, we obtain some $\mathbb{A}$-numerical radius inequalities of operator matrices where $\mathbb{A}$ is the operator diagonal matrix with diagonal entries are positive operator $A$. Some other related results are also investigated.
